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\begin_layout Title
Language Learning Diary - Part Four
\end_layout
\begin_layout Date
Sept 2021 - Dec 2021
\end_layout
\begin_layout Author
Linas Vepstas
\end_layout
\begin_layout Abstract
The language-learning effort involves research and software development
to implement the ideas concerning unsupervised learning of grammar, syntax
and semantics from corpora.
This document contains supplementary notes and a loosely-organized semi-chronol
ogical diary of results.
The notes here might not always makes sense; they are a short-hand for
my own benefit, rather than aimed at you, dear reader!
\end_layout
\begin_layout Section*
Introduction
\end_layout
\begin_layout Standard
Part Four of the diary on the language-learning effort continues work on
the English dataset.
\end_layout
\begin_layout Section*
Summary Conclusions
\end_layout
\begin_layout Standard
A summary of what is found in this part of the diary:
\end_layout
\begin_layout Itemize
Connector sequences or
\begin_inset Quotes eld
\end_inset
disjuncts
\begin_inset Quotes erd
\end_inset
are the
\begin_inset Quotes eld
\end_inset
jigsaw pieces
\begin_inset Quotes erd
\end_inset
extracted from maximum planar spanning-graph (MPG) parses of English sentences.
How many connectors are there on a typical jigsaw piece? Answer: 2.25 on
average.
These are closely modeled by a log-normal distribution.
This is good news for English, where we expect nouns to typically have
1, 2 or 3 connectors, and verbs and prepositions to have 2,3,4.
Adjectives, adverbs and determiners typically have only 1 connector.
Thus the observed distribution matches what one would expect to find.
\end_layout
\begin_layout Itemize
The number of words having any given number of connector sequences also
follows a log-normal distribution.
\end_layout
\begin_layout Itemize
The merger of some top-ranked similar words is explored in detail.
For example, the merger of
\begin_inset Quotes eld
\end_inset
is
\begin_inset Quotes erd
\end_inset
-
\begin_inset Quotes erd
\end_inset
was
\begin_inset Quotes erd
\end_inset
into one word-class.
It seems to go well.
\end_layout
\begin_layout Itemize
It appears that there are cliques or almost-cliques of similar words.
That is, not just word pairs, but groups of 3 or 4 or more words that are
all similar to one-another.
This suggests that such
\begin_inset Quotes eld
\end_inset
in-groups
\begin_inset Quotes erd
\end_inset
of similar words should be merged.
A half-dozen different such in-groups are explored in detail.
They look pretty good.
\end_layout
\begin_layout Itemize
The above leads to a break-through, an important advance in the theory.
One must merge together not only groups of similar words, but only those
disjuncts that are shared by a majority of the words in the in-group.
This is a two-step process: first, an in-group of similar words is selected.
Then, one looks to see what traits (disjuncts) the members of that in-group
have in common.
Only those traits that most group members share are voted into the group.
This solves an important clustering problem: it generalizes, without generalizi
ng over-broadly.
I think this is a major advance in the theory, here.
\end_layout
\begin_layout Itemize
I believe that the result of merging as described above corresponds (strongly)
to word-senses.
(Or it should correspond.) This remains unexplored.
\end_layout
\begin_layout Itemize
How big should an in-group be? The sizes of a dozen different groups are
explored, as a function of the similarity between group members.
It appears that, as one loosens the restrictions on group membership, the
size of the group grows at first very slowly (not at all) and then grows
explosively.
The ideal group size is then the largest group below the explosive-growth
threshold.
\end_layout
\begin_layout Itemize
A good judgment of similarity is needed.
This was explored in great depth in the Diary Part Three.
The mutual information (MI) survives as a good way of judging similarity.
Below, it is discovered that an even better judgment is given by the average
of the MI and the log-frequency.
That is, extremely rare words can have a huge MI, but this is boring, because
the words are rare.
We want to know what words are common (frequent) and also have a large
MI.
This is provided by the average.
Pulling it all together, this results in a square-root in the expression:
\begin_inset Formula
\[
\mbox{ranked}MI\left(w,u\right)=\log_{2}\frac{f\left(w,u\right)}{\sqrt{f\left(w\right)f\left(u\right)}}
\]
\end_inset
where
\begin_inset Formula $f$
\end_inset
is effectively a dot-product.
See below for details.
This is...
surprising, unheard-of in the literature (I've never seen it before).
Its got some nice properties, including being scale free (thus suggesting
it lives on a projective space.
Perhaps some information-theoretic analog of the Fubini-Study metric? Mathemati
cally, its quite intriguing.) Again, this is a pretty big break-through,
as compared to earlier efforts.
\end_layout
\begin_layout Itemize
The above ranked-MI is explored in considerable detail for the English dataset.
It looks pretty good.
\end_layout
\begin_layout Itemize
This part of the diary ends with the first mega-merge, where the top two-thousan
d most similar and most highly ranked words (similarity measured by ranked-MI)
are merged together according to the in-group algo above.
It
\begin_inset Quotes eld
\end_inset
works
\begin_inset Quotes erd
\end_inset
, in that it doesn't crash, and the results still look reasonable after
a few thousand merges (and many days of CPU time.) Thus, the time is ripe
for exploring in detail the results of this merge.
This is done in the next part, Diary Part Five.
But first, an assortment of
\begin_inset Quotes eld
\end_inset
minor
\begin_inset Quotes erd
\end_inset
(but difficult) bugs have to be fixed (and mostly have been!? Tune in next
week for the continuing adventures...)
\end_layout
\begin_layout Standard
To recap: two important things are found.
First, there appears to be a major break-through: the in-group shared-trait
merge algorithm is discovered, and it seems very promising.
Next, averaging together the MI with the word-frequency gives the rankd-MI
similarity, which seems to provide an ideal way of ranking frequent similar
words.
\end_layout
\begin_layout Subsection*
TODO List
\end_layout
\begin_layout Standard
Some items previously explored, but worth looking at again, with the latest
datasets.
\end_layout
\begin_layout Itemize
Words with the lowest self-MI - what are they? What do they mean?
\end_layout
\begin_layout Section*
Expt-4/5/6 – Miscellany – Sept 2021
\end_layout
\begin_layout Standard
Diary Part Three carried out the bulk of experiment-4 with trimming until
it was discovered that trimming to a minimum support of two is even better.
Assorted data analysis was done.
There are still a few more interesting questions about those datasets.
\end_layout
\begin_layout Subsection*
Length of disjuncts
\end_layout
\begin_layout Standard
For a given length of disjunct, how many sections have a disjunct of that
length? (Counted with multiplicity) Previously, in Diary Part Two page
14 this was a Gaussian, centered at 8.
But this was for a fake language, not for English.
Based on what we expect for English, 8 is an alarmingly large number.
So, some graphs:
\begin_inset Foot
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Data for graphs prepared with `utils/similarity-graphs.scm`
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\begin_layout Standard
\align center
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filename en-sims-p3/djlen-dist.eps
width 80text%
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\begin_layout Standard
The above shows the number of disjuncts of a given length.
That is, fixing the length, just count how many disjuncts there are.
Also shown is an eyeballed fit using the log-normal distribution.
As before, this is defined as
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
N\left(x;\mu,\sigma\right)=\frac{1}{x\sigma\sqrt{2\pi}}\exp\left(-\frac{\left(\ln x-\mu\right)^{2}}{2\sigma^{2}}\right)
\]
\end_inset
In this graph, shown is
\begin_inset Formula $\mu=0.81$
\end_inset
and
\begin_inset Formula $\sigma=0.27$
\end_inset
.
Note that
\begin_inset Formula $\exp0.81\approx2.25$
\end_inset
and so we can take the average length of a disjunct as 2.25.
This is really pretty nice for English, I guess – we expect common-sense
lengths: transitive verbs with a length of 2 (subject, object); common
nouns with a length of 2 (determiner, verb-connector) or 3 (determiner,
adjective, verb connector); both determiners and modifiers (adjectives,
adverbs) should have a length of 1.
Punctuation, ditransitive verbs, quotations, etc.
have more complex structure.
So above looks healthy.
\end_layout
\begin_layout Standard
How about the observation count of the number of words that have some disjunct
length? Below:
\end_layout
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width 80text%
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\begin_layout Standard
So this shows three very similar curves.
These are:
\end_layout
\begin_layout Description
number: How many disjuncts there are of a given length.
\end_layout
\begin_layout Description
support: How many sections there are, with that section having a disjunct
of the given length.
\end_layout
\begin_layout Description
count: The number of observations of sections having a disjunct of the given
length.
\end_layout
\begin_layout Standard
Recall that a
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section
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is just a word-disjunct pair.
Thus,
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support
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is when we tally 1 if a section exists, else 0, and
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count
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\end_inset
is how many times that particular pair was observed.
\end_layout
\begin_layout Standard
Looking at that graph, all three have almost the same log-normal distribution,
with the mean inching ever so slightly lower.
The nice behavior persists.
\end_layout
\begin_layout Standard
One last graph: for any given disjunct length, how many unique words are
there that have a disjunct with that length? Shown below.
\end_layout
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filename en-sims-p3/djlen-word-dist.eps
width 80text%
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\begin_layout Standard
So its similar to the above, but wider.
Note that any given word might be counted repeatedly, since it might have
disjuncts of various different lengths.
So, to read this graph correctly: there are very few words having disjuncts
of length 8 (two of them, to be precise).
Most words don't have that many disjuncts.
Here's the table:
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That is, there are 5446 words that have disjuncts of length 1, and 14146
words with disjuncts of length 2, and so on.
Recall this dataset has a total of 15083 words, and so apparently, there
are some words that do NOT have any disjuncts of length 2! This is somewhat
surprising.
I wonder what those are.
Lets take a quick look.
\end_layout
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There are
\begin_inset Formula $937=15083-14146$
\end_inset
words that do NOT have disjuncts of length two.
Looking over the list, they are junk.
Here's the top-10, their observation count and their rank in the list of
all words.
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http://pglaf.org
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\begin_layout Standard
So ..
these do look fairly skanky.
The rankings are ...
well, out of 15K words, these rankings are fairly high.
They are legitimate words, and are obviously seen fairly often in the texts.
Yet, presumably, they occur in some fairly specialized constructions.
For example, pglaf almost certainly appears in boilerplate, and as such
this text will be very rigid in its structure.
Perhaps, then, not surprising that such rigidity might be missing a common
disjunct size.
\end_layout
\begin_layout Standard
Anyway, we conclude that the distributions look healthy and behave as expected.
There are no obvious faults to be seen.
\end_layout
\begin_layout Subsection*
Rankings of mergeable words
\end_layout
\begin_layout Standard
That top-40 list of words to merged – what is the ranking of those words?
That is, when we go to compute similarities, how deep should they be computed?
Here, we assume common-MI provides the merge suggestion, and ranking is
by count, as always.
\end_layout
\begin_layout Standard
Ugh.
Yes, I could, should provide graphs here.
I'm lazy, so not today.
Basically, the large majority (maybe 90%?) of the top-100 ranked pairs
involved words in the top-200 count rankings.
Exceptions are (i,ii) and (Old, New) the words of which are ranked around
500, and (don't,don’t), and (didn’t,don’t) whose words are ranked around
300, (ii,iv) and (iii,iv) and (------,--------) whose words rank around
1000.
\end_layout
\begin_layout Standard
Conclude: it is safe to compute common-MI out to about 200 or so, and then
merge the top-100 out of this list.
\end_layout
\begin_layout Subsection*
Word Similarity with Shapes
\end_layout
\begin_layout Standard
Consistent merging requires that merging must be done with shapes.
But we judged word similarity without shapes.
What happens if we judge word similarity with shapes? After a quick look,
it appears to be substantially similar.
Many (most?) of the same pairs show up in the top-60 list, with similar
rankings.
There are some notable differences, some apparently making things worse,
others making things better.
\end_layout
\begin_layout Subsection*
Word Similarity without Shapes
\end_layout
\begin_layout Standard
FYI.
Of the top-ranked 1200 words, there were 51990 word pairs with no overlap
whatsoever, and 668610 with some overlap.
The total is as expected, a triangle-number:
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\xout off
\uuline off
\uwave off
\noun off
\color none
668610 + 51990 = 720600 = 1200 * 1201 / 2.
\end_layout
\begin_layout Section*
Expt-7 – Merging – Sept 2021
\end_layout
\begin_layout Standard
Time to open a new chapter.
We are ready to merge word-pairs, with a mostly-trustworthy dataset.
The goal here will be to merge just one word at a time, by hand, and see
what happens.
We're doing this because of the disastrously bad July 2021 merge attempt,
which generated complete garbage, quite in contrast to the merges from
previous years.
\end_layout
\begin_layout Standard
Part of the reason for the failure of the July merge was that the merge
threshold was set much too low.
Part of the problem is that the datasets had too much grunge in them; they
needed to be trimmed.
Part of the problem is that the default merge used a proxy for the common-MI
value, based on ranking.
Probably most of the failure can be ascribed to the first part: the merge
threshold was set too low.
\end_layout
\begin_layout Standard
We've never studied the merges carefully, before.
Mostly, they seemed to
\begin_inset Quotes eld
\end_inset
just work
\begin_inset Quotes erd
\end_inset
, and we unleashed the machinery, and let it go.
The first time, it worked, the second time, it failed.
Anyway, now that we've got a better dataset, its worth looking at these
in detail.
\end_layout
\begin_layout Subsection*
Merge is-was
\end_layout
\begin_layout Standard
The top word-pair is
\begin_inset Quotes eld
\end_inset
is-was
\begin_inset Quotes erd
\end_inset
, from table on page 23 in Diary Part Three.
Lets characterize this.
Before the merge:
\end_layout
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Now, merge the word, but do NOT merge the connectors.
That will be a distinct experiment.
Issues that need to be addressed: Assorted marginals need to be recomputed.
These include:
\end_layout
\begin_layout Itemize
The support.
This is done automatically, its in the code.
\end_layout
\begin_layout Itemize
The MMT marginals.
This is done in the supplementary routines.
\end_layout
\begin_layout Itemize
New cached similarity score, or at least wipe out the old one.
Not just for this pair, but for all pairs with the contributing words.
Not done yet.
\end_layout
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After the merge, we have:
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850619
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</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Perhaps the most interesting result is that more than 3/4ths of the count
was moved over to the merged class.
Compared to how much of the support moved, its clear that the merger involved
the most-frequently observed sections.
\end_layout
\begin_layout Standard
Mystery result: Total number of disjuncts dropped from 205003 to 202922
(as measured by `
\family sans
(pcs 'right-basis-size)
\family default
`) ..
how can this happen? This suggests some bug!? That's a difference of 2081
...
oh, I see.
The basis shrank, because
\family sans
pcs
\family default
is NOT looking at WordClassNodes...
so there are 2081 disjuncts that got moved out of any word, and into the
new WordClassNode.
(`
\family sans
pcs
\family default
` is from `
\family sans
make-pseudo-cset-api
\family default
`) OK.
Unexpected, but OK.
\end_layout
\begin_layout Subsection*
Merge is-was and connectors too
\end_layout
\begin_layout Standard
Merging connectors requires using shapes.
This is, in fact, the right thing to do, and was hard-won.
But this changes everything.
So lets track what's going on.
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
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Task
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Stats
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<row>
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time to load Sections
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\end_inset
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183 secs
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<row>
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RAM RSS after load
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1.5g
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time to explode
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125 secs
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RAM RSS after explode
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3.4g
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right basis size
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1043583
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855718
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<row>
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1922250
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</lyxtabular>
\end_inset
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\end_layout
\begin_layout Standard
\align center
So ...
How many CrossSections do the words
\begin_inset Quotes eld
\end_inset
is
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
was
\begin_inset Quotes erd
\end_inset
appear in? What are their counts?
\begin_inset VSpace defskip
\end_inset
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="5">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
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is
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union
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18556
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167112
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203939
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<row>
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\begin_inset Text
\begin_layout Plain Layout
Section+Cross support
\end_layout
\end_inset
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\begin_inset Text
\begin_layout Plain Layout
26038
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\end_inset
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\begin_inset Text
\begin_layout Plain Layout
32995
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\begin_inset Text
\begin_layout Plain Layout
46967
\end_layout
\end_inset
</cell>
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\begin_inset Text
\begin_layout Plain Layout
12066
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\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Clustering merges 46967 sects+cross, as expected (this is the union support
size; but in the end only the intersection is merged).
\end_layout
\begin_layout Standard
Issue: the merge code wishes to recompute the MMT.
The merge code was given shapes to work with so it wants to recompute MMT
w/ shapes, but this is not what we're using for similarity.
At any rate, the pipeline needs to be redesigned to use common-MI, instead
of using an MI cutoff.
\end_layout
\begin_layout Subsection*
Expanded Clusters
\end_layout
\begin_layout Standard
Once a cluster has been formed, it will expand.
How does this look like? The top 60 list contains pairs that merge punctuation:
.–? and !–? and .–! There is also: It–He, It–There, It–She, This–It, She–He,
There–He, There–there.
The question is: how does the MI/common-MI change, as the cluster grows?
\end_layout
\begin_layout Standard
The exploration below will not merge connectors.
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
word-pair
\end_layout
\end_inset
</cell>
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\begin_inset Text
\begin_layout Plain Layout
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</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
MI
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
common-MI
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.174
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-1.880
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.251
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.571
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.124
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.705
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
This
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.351
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.677
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.385
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.822
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3.851
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-3.349
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
there
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-3.459
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-12.022
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
So, It–He gets merged first, and the MI's are recalculated.
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
word-pair
\end_layout
\end_inset
</cell>
<cell multicolumn="2" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
MI
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
common-MI
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
6.316
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-3.175
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.143
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-11.642
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
This
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0.753
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-8.946
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.000
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.507
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.206
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.307
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
This
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.240
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.473
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.007
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-5.679
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
there
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-4.130
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-11.231
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Comparing, we see that the mergability scores of There, She, This improve,
and that is a good thing.
The MI of what's left of It has dropped to more of the other words, although
the affinity to There improves.
\end_layout
\begin_layout Standard
Next in line is She–cluster, according to the new rankings.
So lets merge that.
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
word-pair
\end_layout
\end_inset
</cell>
<cell multicolumn="2" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
MI
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
common-MI
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2.664
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-9.239
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3.979
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.442
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
This
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4.214
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-2.414
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $-\infty$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
She
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8.815
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-3.276
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cluster
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
there
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-4.213
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-11.228
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Interestingly, the remainder of what's left to She-He has the MI shoot way
up, and the mergability of this remainder is relatively high.
The MI between the cluster and There, This is unaffected, or even goes
up.
The common-MI scores improve.
Looks like This is next, so do it.
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
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\begin_layout Standard
\align block
As before, two things pop out: the mergability of cluster-There improves,
and what is left of It-This is quite highly mergeable (just like He-She,
last time).
\end_layout
\begin_layout Standard
\align block
What's going on with these remainders? It's worth taking a look.
Below the diagonal are the MI's after the formation of the cluster.
Above the diagonal are the initial MI's, before clustering.
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace defskip
\end_inset
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\begin_layout Standard
Before merging, these were all in the same ballpark.
After merging, we see that the He–She MI really popped! So did It–There.
The rest are meh.
\end_layout
\begin_layout Standard
And again, the common-MI:
\end_layout
\begin_layout Standard
\align center
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\end_inset
\end_layout
\begin_layout Standard
Before the merge, the It–He mergability suggestion was rather quite high;
the rest are OK, but lower down.
\end_layout
\begin_layout Standard
After the merge, the remaining It–There mergability ranking is now very
high, among the highest.
The mergability ranking for He–She is decent...
but a second-order priority.
\end_layout
\begin_layout Subsection*
Revised clustering strategy
\end_layout
\begin_layout Standard
The above analysis suggests a revised clustering strategy.
Let's call it the
\begin_inset Quotes eld
\end_inset
democratic
\begin_inset Quotes erd
\end_inset
strategy, or the
\begin_inset Quotes eld
\end_inset
peer
\begin_inset Quotes erd
\end_inset
strategy.
It goes like this:
\end_layout
\begin_layout Enumerate
Find a word pair with the highest common-MI.
\end_layout
\begin_layout Enumerate
For each word in that initial pair, look for other words that have a regular
MI that is close to that particular word-pair, or better.
\begin_inset Quotes eld
\end_inset
Close
\begin_inset Quotes erd
\end_inset
means
\begin_inset Quotes eld
\end_inset
no worse than 1.0 less
\begin_inset Quotes erd
\end_inset
.
Of these, maybe reject those with a common-MI of more than 5.0 less.
\end_layout
\begin_layout Enumerate
The above list of similar words defines the initial peer group.
\end_layout
\begin_layout Enumerate
Given the peer group, determine which disjuncts belong to it by voting:
if more than half the words share some common disjunct, then this disjunct
will be admitted into the merged cluster.
\end_layout
\begin_layout Enumerate
Perform the merge, merging all of the words into the cluster, and accepting
those disjuncts that have been voted on.
\end_layout
\begin_layout Standard
The above would seem to create a more balanced cluster, as opposed to the
agglomerative merge.
The problem with agglomeration was demonstrated above: what was left on
She–He and on It–There was really quite a lot, and probably should have
been a part of the main cluster.
It wasn't, because agglomeration threw these away, when forming the initial
He–It cluster.
The democratic voting of step 4 appears to solve this problem.
\end_layout
\begin_layout Standard
Democratic voting also appears to address another old bugaboo: how to perform
\begin_inset Quotes eld
\end_inset
generalization
\begin_inset Quotes erd
\end_inset
.
The pure-intersection clustering performs no generalization whatsoever.
The democratic voting allows generalizations to be admitted, when they
weren't before.
So this seems like a big win.
\end_layout
\begin_layout Standard
An open question is how general the generalization should be.
Should it be a majority vote? Perhaps it should be an evaluation of the
intra-cluster MI after the generalization is made? Could there be some
relaxation process, which picks and chooses what disjuncts get admitted,
so as to maximize the intra-cluster MI and to minimize the extra-cluster
(inter-cluster) MI? Right now, voting is easiest.
Perhaps some kind of relaxation algo might be better, in the future.
The relaxation algo is certainly harder.
\end_layout
\begin_layout Standard
We can steal some ideas from the Tonnoni Phi spin-glass canon: the extra-cluster
MI should be best described by an ultrametric, so that the distance from
the cluster, to anything else, has the ultrametric property.
Recall the definition of an ultrametric: it is the distance between two
leaves on a tree.
Two leaves are close if they are on the same branch; they are distant if
they are on different branches.
We want all words in a cluster to not only be close, but to be
\begin_inset Quotes eld
\end_inset
maximally far away
\begin_inset Quotes erd
\end_inset
from anything else, where
\begin_inset Quotes eld
\end_inset
maximally far
\begin_inset Quotes erd
\end_inset
s intended in the ultrametric sense.
(The ultrametric appears in the theory of spin glasses.
It is the
\begin_inset Quotes eld
\end_inset
obvious
\begin_inset Quotes erd
\end_inset
metric for describing human brains in a social network: Every neuron in
my head is much more closely connected to every other neuron in my head,
than it is to your head.
The only connection between my head and yours is the fact that you are
reading these words.
That is both a spin-glass ultra-metric, and also describes there the lest
cruel cut can be made.
Phew.
Sorry for the digression, but this seems important.)
\end_layout
\begin_layout Subsection*
Word-sense disambiguation
\end_layout
\begin_layout Standard
Issue: If we compute MI and common-MI using only Sections, and not Shapes,
but then do a proper merge (i.e.
merging connectors) then we have a post-merge issue: the new sections will
have have disjuncts with the clustered connectors in them.
\end_layout
\begin_layout Standard
This appears to cause several issues, but does it?
\end_layout
\begin_layout Standard
First issue: When the MI's get recomputed, the shape object will be used.
So this is a bug, we need to use the non-shape object when recomputing
the MI.
So this needs to be passed around as a distinct argument to the functions.
\end_layout
\begin_layout Standard
Second issue: When the MI's get recomputed, it might seem that connector
sequences that should have been comparable are no longer being compared,
because one connector sequence has a plain word, while another has a
\family sans
WordClass
\family default
.
Upon further reflection, this is NOT an issue.
Connector merging means that all of the various connector sequences have
been updated (
\begin_inset Quotes eld
\end_inset
correctly
\begin_inset Quotes erd
\end_inset
) with the new
\family sans
WordClass
\family default
, so the sequences remain comparable.
Those that have NOT been updated MUST be considered as belonging to a distinct
word-sense.
\end_layout
\begin_layout Standard
In particular, that means that the correct connector merge code automatically
handles word-sense disambiguation: whatever has not been merged, including
unmerged connectors, MUST be understood to belong to a word-sense that
is distinct from the
\family sans
WordClass
\family default
.
\end_layout
\begin_layout Standard
Conclude: no issue here, except to be careful in recomputing the MI.
\end_layout
\begin_layout Subsection*
Conclusion to Expt-7
\end_layout
\begin_layout Standard
Looks like everything works great.
The functional review provoked a code review, both the functional review
and the code review pass, it seems that merging works great.
Caveat: at least the non-connector-merge variant works great.
The connector-merge code is really complicated, and was developed and debugged
during the random-corpus exploration phase.
It was completed, with no known bugs, but it is just complicated enough
and squonky enough that perhaps there are issues.
There is a test-suite of 13 unit tests.
These pass.
So I guess its pretty tight?
\end_layout
\begin_layout Standard
Examination of the agglomerative clustering strategy exposes it's weakness
(well-known in the industry) However, unlike the conventional clustering
algos, we have the ability to pick and choose, via
\begin_inset Quotes eld
\end_inset
democratic voting
\begin_inset Quotes erd
\end_inset
, which disjuncts get admitted into the cluster.
This appears to address an important open issue, of (a) a way of performing
generalization, and (b) a good way way of performing generalization.
The earlier fuzzy-mixin performed generalization, but it was fairly non-selecti
ve, and some naive MI calculations seemed to indicate that it always made
things worse.
In particular, it made word-sense disambiguation ugly.
So this new democratic algo appears to be a major conceptual improvement.
\end_layout
\begin_layout Section*
Clique Sizes (Oct 2021)
\end_layout
\begin_layout Standard
The democratic-voting idea suggests that an initial in-group needs to be
selected.
This in-group will be a clique or an almost-clique.
But how are we to find it? How similar do words need to be, in order to
belong to an in-group? Here, we explore the size of the clique, vs.
the allowed variation of MI within the clique.
\end_layout
\begin_layout Standard
Consider some given initial word-pair, and a threshold
\begin_inset Formula $\varepsilon$
\end_inset
.
The initial pair has some initial value of common-MI
\begin_inset Formula $S_{0}$
\end_inset
.
A search is performed to find words that have a common-MI greater than
\begin_inset Formula $S_{0}-\varepsilon$
\end_inset
to at least 70% of the members of the current in-group.
To admit a third word into the ingroup, the common-MI must be greater than
\begin_inset Formula $S_{0}-\varepsilon$
\end_inset
to both the current members.
To admit a fourth word, the threshold must be exceeded to at least two
of the three current members, and so on.
The formula is
\begin_inset Formula $vote=\left\lfloor 0.7n+0.5\right\rfloor $
\end_inset
where
\begin_inset Formula $n$
\end_inset
is the number of members in the current in-group.
In general, the larger that
\begin_inset Formula $\varepsilon$
\end_inset
gets, the larger the ingroup will be.
The process is not monotonic, since it depends on the order in which words
are added.
For small
\begin_inset Formula $\varepsilon$
\end_inset
, a tight-knit grouped might be formed.
As
\begin_inset Formula $\varepsilon$
\end_inset
gets larger, one of the early members might be quite different, and becoming
a peer to it might be a challenge, thus decreasing the size of the in-group!
These decreases are visible in the chart below.
To avoid this effect, the words are ranked by frequency first, so that
the most frequent words are considered first.
\end_layout
\begin_layout Subsection*
Common-MI in-groups
\end_layout
\begin_layout Standard
The chart below shows the results for eight different initial word-pairs.
All eight of these appear in the top-15 list of pairs with the highest
common-MI.
Many are punctuation; this is inevitable, as punctuation is very frequent.
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename p4-en-clique/ingroup-size.eps
width 80col%
\end_inset
\end_layout
\begin_layout Standard
So...
interesting ...
There are two asymptotes:
\begin_inset Quotes eld
\end_inset
she-he
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
in-of
\begin_inset Quotes erd
\end_inset
are one, and all the others land on the other.
Note that the asymptotes are just lists of garbage words.
Still, its curious that there are two.
Not shown in the graph: experimentally, the asymptote is almost exactly
given by
\begin_inset Formula $\exp\left(\varepsilon/2\right)$
\end_inset
.
Missing theory: why? Why the natural exp? Why not something else, like
\begin_inset Formula $2^{\varepsilon}$
\end_inset
?
\end_layout
\begin_layout Standard
Some clusters grow easily -
\begin_inset Quotes eld
\end_inset
she-he'
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
in-of
\begin_inset Quotes erd
\end_inset
both grew quickly.
\begin_inset Quotes eld
\end_inset
Is-was
\begin_inset Quotes erd
\end_inset
took longer to take off.
Here are some samples, taken at the maximum value of
\begin_inset Formula $\varepsilon$
\end_inset
at which the results look good.
That is, for larger
\begin_inset Formula $\varepsilon$
\end_inset
, the ingroup starts looking ugly.
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
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epsilon
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\begin_inset Text
\begin_layout Plain Layout
size
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\end_inset
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\begin_inset Text
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ingroup
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<row>
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\begin_inset Text
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3.0
\end_layout
\end_inset
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\begin_inset Text
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10
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\begin_inset Text
\begin_layout Plain Layout
might must may should will could would had is was
\end_layout
\end_inset
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3.0
\end_layout
\end_inset
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7
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when so for as that and but
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3.4
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\end_inset
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13
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\begin_inset Text
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from by with at on for as not that to and in of
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\end_inset
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1.6
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5
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\begin_inset Text
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they it I she he
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5.0
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9
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\begin_inset Text
\begin_layout Plain Layout
: ! _ " ” .
###LEFT-WALL### , ;
\end_layout
\end_inset
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5.0
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10
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: ! _ " ; ” ###LEFT-WALL### , .
?
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\end_inset
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\begin_inset Text
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5.9
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\end_inset
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\begin_inset Text
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7
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\begin_inset Text
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] ( [ * _ + —
\end_layout
\end_inset
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<row>
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\begin_inset Text
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6.7
\end_layout
\end_inset
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\begin_inset Text
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8
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\begin_inset Text
\begin_layout Plain Layout
R M $ D N p i ii
\end_layout
\end_inset
</cell>
</row>
<row>
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\begin_inset Text
\begin_layout Plain Layout
2.3
\end_layout
\end_inset
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
13
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Yes We This They You What She And The He I It There
\end_layout
\end_inset
</cell>
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</lyxtabular>
\end_inset
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
The initial seeds that start the ingroup appear as the last two members
of the lists.
Note that some lists end up being similar, even though the seed-pairs are
different.
\end_layout
\begin_layout Standard
The two collections of punctuation started with different seed pairs, but
converged to the same place.
One started with comma-semicolon, the other started with period-question-mark.
Similar results for the prepositions.
The
\begin_inset Quotes eld
\end_inset
and-but
\begin_inset Quotes erd
\end_inset
forms the seed in the first group, but most of that group reappears in
the ingroup around the seed
\begin_inset Quotes eld
\end_inset
in-of
\begin_inset Quotes erd
\end_inset
.
The last one is curious – its all sentence-starter words (That's why they
are capitalized).
\end_layout
\begin_layout Standard
The above does not teach a clear lesson in how to pick
\begin_inset Formula $\varepsilon$
\end_inset
.
Picking a fixed value does not seem like a good idea.
A reasonable merge strategy might be to start with
\begin_inset Formula $\varepsilon=1$
\end_inset
, merge what there is, and then enlarge some more.
As always, the question is when to stop enlarging....
no answer for that, yet.
There are two indicators: stop enlarging just before the size of the group
increases rapidly, and stop enlarging when the size of the group suddenly
drops.
This seems to be viable – the calculations are relatively fast.
\end_layout
\begin_layout Subsection*
Plain-MI in-groups
\end_layout
\begin_layout Standard
Wait ...
we did the wrong thing.
The above used common-MI to determine similarity to the in-group.
Perhaps just the regular-MI should be used.
That is, common-MI is great for identifying the initial word-pair to form
the seed of the clique, but perhaps regular MI is better suited to actual
similarity.
Here are the graphs, again, this time using regular MI.
Note that the threshold goes negative.
For example, for
\begin_inset Formula $\varepsilon=0$
\end_inset
for the initial seed
\begin_inset Quotes eld
\end_inset
is-was
\begin_inset Quotes erd
\end_inset
, there ae already four members of the ingroup.
This means that there ar two other words whose MI to
\begin_inset Quotes eld
\end_inset
is
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
was
\begin_inset Quotes erd
\end_inset
is higher than the MI between
\begin_inset Quotes eld
\end_inset
is
\begin_inset Quotes erd
\end_inset
and
\begin_inset Quotes eld
\end_inset
was
\begin_inset Quotes erd
\end_inset
.
Cool! Here's the graph:
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename p4-en-clique/in-migrp-size.eps
width 80col%
\end_inset
\end_layout
\begin_layout Standard
So this is very different than the earlier graph.
Still all over the place.
Lets take a sample:
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="3">
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epsilon
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\begin_inset Text
\begin_layout Plain Layout
size
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doesn’t takes isn’t appears wasn’t wasn't seems seemed is was
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nor till until since than or for as and but
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toward towards against through upon into from in of
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thou it's it’s we they she he
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4.0
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13
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\begin_layout Plain Layout
– ...
] — : ! _ " ” .
###LEFT-WALL### , ;
\end_layout
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5.4
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16
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\begin_inset Text
\begin_layout Plain Layout
– ...
… ' ] — : ! _ " ; ” ###LEFT-WALL### , .
?
\end_layout
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5.1
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7
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\begin_inset Text
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– { ] ( [ + —
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11
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b R Y $ E C D N p i ii
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1.8
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10
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\begin_inset Text
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These Here That We This They She He It There
\end_layout
\end_inset
</cell>
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\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
So this has a very different flavor.
With common-MI, we saw words like
\begin_inset Quotes eld
\end_inset
could would should
\begin_inset Quotes erd
\end_inset
being judged similar to
\begin_inset Quotes eld
\end_inset
is was
\begin_inset Quotes erd
\end_inset
.
Here, we see
\begin_inset Quotes eld
\end_inset
appears seems
\begin_inset Quotes erd
\end_inset
showing up, while
\begin_inset Quotes eld
\end_inset
could would
\begin_inset Quotes erd
\end_inset
is entirely absent (and continues to be absent until the ingroup has size
25!) This means that – appearing and seeming is much more like being, but
desires and statements of ideals, like
\begin_inset Quotes eld
\end_inset
could should
\begin_inset Quotes erd
\end_inset
occur far more frequently in the text.
(High frequency words boost the common-MI but have no effect on plain MI.)
So these are two very different semantic directions to go off in! How to
resolve this? What, exactly, are we doing here?
\end_layout
\begin_layout Standard
The other groups seem to have a slightly different flavor, but nothing quite
as distinct.
Gut impulse is to say that common-MI is a better classifier, even though
there's some semantically interesting stuff happening with regular-MI.
But we are not yet ready to pursue semantics; we're still working on syntax.
\end_layout
\begin_layout Subsection*
In-group ranking spread
\end_layout
\begin_layout Standard
Words are added to the in-group one at a time, starting with the most-frequently
occurring words.
By the time that the construction of the in-group is done, what is the
difference between the highest-ranked word in the in-group, and the lowest-rank
ed? This is graphed below.
It's done with common-MI to determine in-group membership.
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename p4-en-clique/ingroup-spread.eps
width 80col%
\end_inset
\end_layout
\begin_layout Standard
What this chart shows is that when the in-group has fewer than 10 members,
all of those members are within 100 of each other in the word-frequency
ranking (with exceptions as visible in the graph.) Note this is
\emph on
not
\emph default
a function, the lines can zig-zag left and right.
Some cliques are tighter than others.
\end_layout
\begin_layout Standard
Recommendations: if we're going to compute similarity, do so in a band of
about 200 from the diagonal.
\end_layout
\begin_layout Subsection*
Mid-level pairs
\end_layout
\begin_layout Standard
The above results were all for seed word-pairs that were top-ranked in terms
of common-MI.
How about something from the middle? Here are some seed word-pairs whose
common-MI is about 4 less than the top-ranked pairs above.
They are approximate in the 10K'th position of all ranked pairs (ranked
by common-MI).
They still look pretty good, in terms of English.
Those that have an MI of 8 below the top-ranked pair start looking like
garbage.
The only problem with this exploration is that ...
pairs that are 10K down are ...
far far from consideration.
Words in them are likely to get swept up much earlier.
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename p4-en-clique/ingroup-middle.eps
width 80col%
\end_inset
\end_layout
\begin_layout Standard
Shown for comparison is the old
\begin_inset Quotes eld
\end_inset
is-was
\begin_inset Quotes erd
\end_inset
group.
Note that the ingroups are quite large even for negative
\begin_inset Formula $\varepsilon$
\end_inset
.
This just says that these seed-pairs are likely to be swept up in earlier
in-group formations.
\end_layout
\begin_layout Standard
Let's assess their health.
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
epsilon
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
size
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ingroup
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-0.7
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
5
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
looked had was spoke sat
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0.6
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
glance look smile
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-0.3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
11
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
church United sea city country people house world most town earth
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-0.6
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
5
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
end head same door house
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Well ...
mixed bag.
In the first row,
\begin_inset Quotes eld
\end_inset
had was
\begin_inset Quotes erd
\end_inset
are likely to be swept up in some other group, leaving
\begin_inset Quotes eld
\end_inset
looked spoke sat
\begin_inset Quotes erd
\end_inset
fairly healthy.
In the third row,
\begin_inset Quotes eld
\end_inset
most
\begin_inset Quotes erd
\end_inset
is likely be be swept up in some other in-group; what's left looks OK.
The last row looks haphazard.
Presumably
\begin_inset Quotes eld
\end_inset
same
\begin_inset Quotes erd
\end_inset
will end up in some other in-group, but what about
\begin_inset Quotes eld
\end_inset
end
\begin_inset Quotes erd
\end_inset
?
\end_layout
\begin_layout Standard
At this point, there seems to be no choice: we have to run the earlier clusters,
and then see what's left over.
Perhaps this can be done manually? So we can get a better idea? That requires
running 10-20 clusters by hand, and then repeating this exercise.
\end_layout
\begin_layout Section*
Expt-8 Merging Farther (Oct 2021)
\end_layout
\begin_layout Standard
Resuming where expt-7 left off.
This time, do merge with shapes, and get further down the process.
Lay groundwork for the cliques above.
\end_layout
\begin_layout Standard
One major issue is that, after merging connectors, all of the previous similarit
y computations are rendered invalid.
We need to loop over all merged connectors, and recompute those similarities,
if they are/were in the range of computable similarities...
then, after that we need to re-rank, to find the next items in the list.
\end_layout
\begin_layout Standard
Done.
Fixed some bugs, seems to work well, happy and healthy ...
code being created in `
\family sans
agglo-rank.scm
\family default
` based on results and outline.
Nothing notable pops out, other than it looks great! Yahoo! We're rolling
again!
\end_layout
\begin_layout Section*
Expt-9 Ranked Merge Development (Oct 2021)
\end_layout
\begin_layout Standard
So since expt-8 went so swimmingly, ranked merge development should go smoothly,
too, right? Heh.
Not so lucky.
\end_layout
\begin_layout Standard
Confusion.
We are calculating the marginal similarity as
\begin_inset Formula
\[
P\left(w\right)=\frac{\sum_{d}P\left(w,d\right)P\left(*,d\right)}{\sum_{d}P\left(*,d\right)P\left(*,d\right)}
\]
\end_inset
The normalization here is so that
\begin_inset Formula $P\left(*\right)=1$
\end_inset
which is what we want so that we can interpret these things as probabilities.
\end_layout
\begin_layout Standard
What is the value of
\begin_inset Formula $\sum_{d}P\left(*,d\right)P\left(*,d\right)$
\end_inset
? I think we want to add this as a constant to common-MI.
As a constant, it changes nothing, but it prevents common-MI from being
always negative.
We don't have it handy because we are not storing P's, we are storing N's;
we need to compute it.
It is
\begin_inset Formula
\[
Q=-\log_{2}\sum_{d}P\left(*,d\right)P\left(*,d\right)=-\log_{2}\frac{\sum_{d}N\left(*,d\right)N\left(*,d\right)}{\left(\sum_{d}N\left(*,d\right)\right)^{2}}
\]
\end_inset
Wow.
The mind boggles.
Numerically, for the t1234 dataset, it is 11.946 which is actually a healthy
value.
\end_layout
\begin_layout Standard
The mind boggles because this is...
well, its a scale parameter.
It's also a mean-square.
It's a screwy matrix norm of some kind.
It feels like there should be some kind of physical interpretation for
it.
Some kind of graph spectral foo-bar, but I don't know what that is.
\end_layout
\begin_layout Standard
There's a generic problem here: we've got some kind of graph spectral something-
or-other here, but I don't know that theory.
There's a hint that its simple, elegant, and should have some obvious interpret
ation.
Fer Chris sake, the last figure of Part Three was a Gaussian! There's got
to be some kind of generic theorems on this stuff.
\end_layout
\begin_layout Standard
Note the common-MI was not scale invariant.
It was defined as
\begin_inset Formula
\[
\mbox{common}MI\left(w,u\right)=\log_{2}\frac{f\left(w,u\right)f\left(*,*\right)}{\sqrt{f\left(w\right)f\left(u\right)}}
\]
\end_inset
with
\begin_inset Formula
\[
f\left(w,u\right)=\sum_{d}P\left(w,d\right)P\left(u,d\right)
\]
\end_inset
This suggests that scale invariance can be restored by adding
\begin_inset Formula $Q$
\end_inset
...
\end_layout
\begin_layout Subsection*
Ranked MI
\end_layout
\begin_layout Standard
OK, so the above ruminations suggest that using ranked-MI is better than
using common MI.
We define this as
\begin_inset Formula
\begin{align*}
\mbox{ranked}MI\left(w,u\right)= & \mbox{common}MI\left(w,u\right)+Q\\
= & \log_{2}\frac{f\left(w,u\right)}{\sqrt{f\left(w\right)f\left(u\right)}}
\end{align*}
\end_inset
This is now scale invariant, in that we can multiply
\begin_inset Formula $f$
\end_inset
by any constant, and the ranked-MI is unchanged.
So its projective...
Projective suggests that this is some information-theoretic analog of the
Fubini-Study metric, or something like that.
What is the mathematics of this? What is the physical interpretation of
it?
\end_layout
\begin_layout Subsection*
Ranking cutoffs
\end_layout
\begin_layout Standard
As a practical application, ranking works best if we add cut-offs: reject
all pairs with an MI of less than 4.0.
This knocks out some pairs that have a high ranked-MI but otherwise crappy
MI.
\end_layout
\begin_layout Standard
There's also another
\shape italic
de facto
\shape default
filter at play: if we compute sims only for the top-200 words, any highly
similar words that aren't in the top-200 simply won't appear.
For example, the roman numeral `(Word "i")` is ranked 458'th in the list
of words, `(Word "ii")` is ranked 701'th.
They are highly similar: MI=12.52 and a ranked-MI of 9.05 which would have
placed it fourth in the table below.
But they are too far away from the top-200 and so are never considered.
\end_layout
\begin_layout Standard
Worse: they are not even within the diagonal band that is 200 wide, and
so will never be considered...
perhaps the band needs to get wider over time....
\end_layout
\begin_layout Standard
So, with that in mind: looking only at the top-200 words, there are 1338
pairs with an MI of greater than 4.0.
Accepting only those, here's the list of the top-20 word pairs:
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="21" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
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word-pair
\end_layout
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ranked-MI
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MI
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—
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I'm enjoying that both the left-slanting and the right-slanting single and
double quotes show up in this list correctly paired with each-other.
\end_layout
\begin_layout Standard
Lets take a look at what we missed with the MI cutoff.
There are 310 words pairs with an MI between 3 and 4.
The top-5 in this list are:
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Notable is the-a, which appears 8th in this list, with ranked-MI = 7.4818
and MI = 3.1485.
Capitalized The A appear 15th with ranked-MI = 7.2114 and MI = 3.4420.
\end_layout
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One more time, for MI between 2 and 3:
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###LEFT-WALL###
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So this looks pretty reasonable until we get to the last entry, which is
pretty crappy.
Except for that one, the next 15 look pretty decent.
So ...
things seem healthy.
\end_layout
\begin_layout Standard
What if we are more demanding? What if we insist on an MI of greater than
6, which would knock out most of the words in the early list? Here we go:
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7.1761
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\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
6.2910
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Yikes! The next four entitles are also punctuation.
I think the corpus had a bunch of ASCII-formatted tables in it.
These are reasonable suggestions, but are actually ..
boring.
So setting MI=4 for this dataset seems like the right thing to do.
\end_layout
\begin_layout Standard
Of course, long-term, this MI threshold needs to be auto-discovered.
However, 4 has been working great for me for the last 5-6 years, so ..
hey.
It's dataset-size dependent, and all my datasets end up being as big as
I can make them and still be manageable.
\end_layout
\begin_layout Subsection*
Duplicate Cluster Names
\end_layout
\begin_layout Standard
OK, so, during merge, after 26 previous merges, we hit a merge of (`###LEFT-WALL
###`, `:`) which is reasonable, except that we'd already merged these two
before, at iteration 12.
So what is being merged now is presumably the left-overs of that earlier
merge.
Is this sane? Is this a bug? Some details.
\end_layout
\begin_layout Standard
Previous: at round 12, merged`###LEFT-WALL###`, `:` from a start of ranked-MI
= 7.7349 MI = 4.1172.
\end_layout
\begin_layout Standard
At round 26, we merge (`]`, `:`) because they have ranked-MI = 6.9107 MI
= 8.5029.
This apparently splits off enough of the colon that what is left over is
now similar to the left-overs from LEFT-WALL.
(Although I'm confused? Didn't the overlap merge pre-emptively remove all
traces of similarity? So how did this come back?)
\end_layout
\begin_layout Standard
So, at round 27, we get ranked-MI = 7.0566 MI = 6.5282 for `###LEFT-WALL###`,
`:` and so these dregs get merged again.
Surprise!
\end_layout
\begin_layout Standard
The confusion: the overlap merge should have clobbered the dot product,
and left the dregs completely orthogonal to the cluster.
Because overlap merge means to sum over all basis elements that are non-zero
in common, which are the *only* basis elements contributing to the dot
product.
So, post-merge, the cosines should be exactly zero.
All three of them: the cluster should be orthogonal to each of the contributing
words, which are orthogonal to each-other.
Further stripping out disjuncts from the colon should not have changed
it's orthogonality to either the first cluster, or to the left wall.
\end_layout
\begin_layout Standard
So it seems like we've got a bug somewhere.
Is that correct? Is it possible that connector merging brought these two
back in parallel? Lets find out...
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
word-pair
\end_layout
\end_inset
</cell>
<cell multicolumn="2" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
cosine
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
overlap
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
###LEFT-WALL###
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
:
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0.3317
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8.746e-4
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
class
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
:
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0.3584
\end_layout
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0.0103
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
###LEFT-WALL###
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
class
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0.4809
\end_layout
\end_inset
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
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9.610e-4
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
So some of the overlaps are tiny, but the cosine is huge! The only way this
can happen is if most of the disjuncts have very small counts, so that
the vector length is unaffected by them (these appear in the denominator
of the cosine), while the overlapping disjuncts are the ones with the high
counts.
\end_layout
\begin_layout Standard
And indeed that is what happened! There are 56 entries in the overlap of
left-wall and colon, out of about 46K.
All 56 of these are CrossSections.
All have large counts.
All have Shapes involving a
\family sans
WordClassNode
\family default
.
Thus, although merger will orthogonalize vectors, later connector merges
can add back parallel components.
Again: this is a sheaf, and its got some kind of torsion or curvature.
The connector-merge is a kind-of parallel transport around a loop, and
bends things around.
I'm pretty sure this is the right way to think about it, but actually writing
out the formal mathematical details of this would be quite the project.
Almost surely a good exercise, as it will clarify what the heck is going
on, but ..
a difficult one.
\end_layout
\begin_layout Standard
On with the show!
\end_layout
\begin_layout Subsection*
In-group Merge Results
\end_layout
\begin_layout Standard
Some early results.
This uses quorum=0.7, so that a disjunct is placed in the cluster of 70%
of the in-group shares that disjunct in common.
The ingroup is selected according to a bunch of hard-coded parameters in
the code, see `cliques.scm` in the 12 Oct 2021 git tree for details.
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace defskip
\end_inset
\begin_inset Tabular
<lyxtabular version="3" rows="14" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
in-group
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
nwords
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
top-rank-MI
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $Q$
\end_inset
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\end_inset
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<row>
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\begin_inset Text
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-
\end_layout
\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
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-
\end_layout
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
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\begin_inset Text
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] ( [ * _ — +
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is was
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as that and but
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\begin_inset Text
\begin_layout Plain Layout
! " ###LEFT-WALL### .
?
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10.466
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There I It He
\end_layout
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10.650
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\begin_inset Text
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They She He It There
\end_layout
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5
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8.6036
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from to in of
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4
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8.1951
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' ‘ “
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3
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8.0408
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this he a the his
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7.9914
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my her the his
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4
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7.8097
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\begin_inset Text
\begin_layout Plain Layout
my this her a the his
\end_layout
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</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
6
\end_layout
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
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7.8352
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</cell>
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\begin_inset Text
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\end_layout
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</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
The
\begin_inset Formula $Q$
\end_inset
reports the
\begin_inset Formula $Q$
\end_inset
value defined up above.
(its called `
\family sans
mmt-q
\family default
` in the code).
The
\begin_inset Formula $Q$
\end_inset
is that after the merge is performed.
Thus, the first row is the initial
\begin_inset Formula $Q$
\end_inset
of the starting dataset.
\end_layout
\begin_layout Standard
There's actually a bug in the code w.r.t.
\begin_inset Formula $Q$
\end_inset
– because it is changing from merge to merge, any cached similarity scores
will use the old
\begin_inset Formula $Q$
\end_inset
from earlier rounds.
These will no longer be correct for the new
\begin_inset Formula $Q$
\end_inset
value, even though the MI is unchanged and the
\begin_inset Formula $\log P$
\end_inset
marginals are unchanged.
So we have to stop adding
\begin_inset Formula $Q$
\end_inset
into the cached scores.
Ooops!
\end_layout
\begin_layout Standard
There's another bug with voting.
After an in-group is selected, as judged by MI, it turns out that only
a small number of disjuncts are shared by more than 70% of the ingroup.
Sometimes less than 1%! These are clustered, but then, out of what's left,
a new very similar in-group is created, because the MI is still high.
This is seen in the last three lines of the table above, and also in the
It-He lines in the table.
\end_layout
\begin_layout Standard
Heh.
Now its stuck in an infinite loop, merging 0 sections each time around!
\end_layout
\begin_layout Standard
Solution would seem to be to kick out the most recent members from the in-group,
until at least 20% of the disjuncts of the smallest member are shared by
all.
The 20% figure allows the smallest member to have five different word-senses
(i.e.
to belong to five different clusters.)
\end_layout
\begin_layout Standard
We shall call this number the
\begin_inset Quotes eld
\end_inset
commonality
\begin_inset Quotes erd
\end_inset
, and request that the ingroup have a minimal commonality.
The code documentation explains this better than here.
\end_layout
\begin_layout Subsection*
In-group commonality
\end_layout
\begin_layout Standard
OK, so this needs further study.
The failing in-group was `There` `It` `He` `They`.
Initially, the following ranked-MI's are observed:
\begin_inset Foot
status collapsed
\begin_layout Plain Layout
Use this code:
\end_layout
\begin_layout Plain Layout
\family sans
(load-atoms-of-type 'SimilarityLink)
\end_layout
\begin_layout Plain Layout
\family sans
(define sap (add-similarity-api covr-obj #f "shape-mi")
\end_layout
\begin_layout Plain Layout
\family sans
(sap 'pair-count (Word "There") (Word "It"))
\end_layout
\begin_layout Plain Layout
The first number is MI, the second is ranked-MI.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="5">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
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\begin_inset Text
\begin_layout Plain Layout
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\begin_inset Text
\begin_layout Plain Layout
There
\end_layout
\end_inset
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\begin_inset Text
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It
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
He
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
They
\end_layout
\end_inset
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\align center
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\end_inset
\end_layout
\begin_layout Standard
After this, there are 5 rounds that merge as documented in the previous
section.
\end_layout
\begin_layout Standard
At round 6, `He` `It` `I` `There` are merged, seeded by `It` and `He`.
At this time, ranked-MI = 8.8665 MI = 4.9165 (`It`, `He`) At this merge,
approx 600 out of 6000 sections each are merged.
\end_layout
\begin_layout Standard
Round 7 is seeded by ranked-MI = 8.6036 MI = 10.873 (`It`, `There`) and merges
`There` `It` `He` `She` `They`.
Approx 20 sections each get merged, so this is already a small number.
\end_layout
\begin_layout Standard
Round 8 is seeded by ranked-MI = 8.6293 MI = 10.875 (`It`, `There`) and merges
`There` `It` `He` `They` with less than 20 sections each contributing.
\end_layout
\begin_layout Standard
Round 9 starts with ranked-MI = 8.6296 MI = 10.878 (`It`, `There`) and attempts
to merge `There` `It` `He` `They`.
The result of this attempt is zero sections contributing! How is this possible?
\end_layout
\begin_layout Standard
If we stop there and look, we get:
\end_layout
\begin_layout Standard
\align center
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\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
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\end_layout
\begin_layout Standard
The negative ranked MI at `It`, `They` shows the problem.
BTW, the regular MI is -2.264 for these two.
Recall that the ingroup is determined by stopping the addition of members
just before membership explodes.
It says nothing about all of the members in the in-group having to have
a high MI.
Perhaps it should?
\end_layout
\begin_layout Standard
Its clear that backing off the one word `They` will resolve the issue.
It's the one halting progress.
The quorum is set at 0.7, so majority vote requires
\begin_inset Formula $\left\lfloor 4\times0.7+0.5\right\rfloor =3$
\end_inset
agreements.
Obviously, none of these will come from `They`, and so `There` `It` `He`
would have to be unanimous.
But they can't be: they were already merged in round 7 and 8.
\end_layout
\begin_layout Standard
Conclude: we have two solutions: reject ingroup members with a negative
MI to other in-group members.
Also apply the commonality requirement.
\end_layout
\begin_layout Subsection*
In-group merge results, restarted
\end_layout
\begin_layout Standard
As above, but restarting with a commonality of 20% and an absolute lower
bound of 1.0 for the ranked-MI.
The Q value is the Q at the start of the merge.
After the merge is completed, Q is recomputed.
Here,
\begin_inset Quotes eld
\end_inset
kick
\begin_inset Quotes erd
\end_inset
in the in-group column means the last member is being kicked out.
That is, in-groups start large, and then members are kicked out until a
suitable commonality is reached.
\end_layout
\begin_layout Standard
Here are the first four merges.
\end_layout
\begin_layout Standard
\align center
\begin_inset VSpace defskip
\end_inset
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14201
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9.55%
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8.449
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11776
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46508
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25.32%
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9.0319
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8.851
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3180
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94563
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3.36%
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8829
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83719
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10.54%
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4842
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55787
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8.68%
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Here are some merges further down the queue.
Merge 18 appears to be the first one accepting three items.
If we had set commonality to 10%, then merge 4 would have been the first.
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mrg
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overlap
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18
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could should will may
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7.4589
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10.908
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1230
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13959
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8.81%
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could should will
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2617
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12707
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20.59%
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19
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are were had did
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4
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7.3664
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10.912
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1180
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32338
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3.65%
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kick did
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3
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4666
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29402
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15.87%
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19
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are were
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2
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3436
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14476
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23.74%
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20
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there There
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2
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7.3611
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10.922
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210
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6136
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3.42%
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21
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There It This That
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4
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8.3244
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10.951
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115
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4914
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2.34%
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kick That
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3
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409
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4244
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9.64%
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21
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There It
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And still further down:
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And again, further down:
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Hmm.
Thoughts about specific merges:
\end_layout
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There are some close shaves, e.g.
merge 96 which proposes something ugly.
Then there's merge 99 which doesn't seem right.
And there's merge 100 which is prettiest in its final form.
Note that these are all late-stage merges.
\end_layout
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Merge 53 is due to some books including many tables.
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General remarks:
\end_layout
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A commonality of 20% sometimes seems to high.
Sometimes seems just right.
Worth trying 10% or 5%.
\end_layout
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A quorum of 0.7 is probably too high! Perhaps 0.5 would be better.
That is, half the members share at least 20% of traits.
\end_layout
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We want a quorum of the members to share a commonality of traits ..
but the relationship of both of these to the MI seems very unclear.
These groups start with very high MI, and yet, seem to have little in common.
How is that? Is it because we are counting commonality wrong?
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We are counting commonality by the
\emph on
number
\emph default
of disjuncts shared.
But the MI is computed by weighting high-count disjuncts highly, and low-count
disjuncts low.
Is there a way to weight the commonality score likewise? But how, exactly?
How do we turn this into a scale-free number? The problem is that, by definitio
n, the count will be zero for some (this is how generalization happens.)
I can't think of a worthy alternate variant of commonality.
\end_layout
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Possible solutions:
\end_layout
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Looks like sometimes commonality drops as words are removed.
This is is interesting and ..
useful.
Seems like a good strategy would be to accept the largest group before
commonality drops! This is cool stuff!
\end_layout
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Perhaps it is time to reintroduce the noise floor, so that disjuncts with
low counts are swept up during the merge.
...
DONE.
\end_layout
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Sooo...
\end_layout
\begin_layout Subsection*
More In-group merge results
\end_layout
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Again.
Set quorum=0.5, commonality=20% and noise-floor = 4.
The first five merge results:
\end_layout
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13152
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6.20 %
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kick _
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4
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388
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11162
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3.48 %
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— + “ ” _
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9.1620
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3.762
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3687
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48332
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7.63 %
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is was
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9.0605
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4184
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14950
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27.99 %
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but and that as
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9.0319
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7.483
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4377
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30763
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14.23 %
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kick as
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3
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3151
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27116
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11.62 %
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but and that as
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5
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? .
LEFT-WALL to it : )
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7
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8.9357
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8.143
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54
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75929
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0.07 %
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354
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75324
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0.47 %
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2629
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74470
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3.53 %
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2051
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65759
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3.12 %
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? .
LEFT-WALL to it
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</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
Clearly visible are two effects: the climb-back-up because commonality dropped,
and the much smaller total dj number, which means most dj's really had
a count of 4 or less.
And we're taking the vote away from them.
\end_layout
\begin_layout Standard
To be clear: the noise-floor says that any section with a count of equal
or less than the floor will be ignored during voting, and will be automerged,
no matter what the outcome of voting.
(Perhaps we should have two distinct noise-floors: one for adjusting counting,
the other for merging?)
\end_layout
\begin_layout Section*
Nov-Dec 2021: The Big Merge
\end_layout
\begin_layout Standard
Ran a long-running merge.
Working with Expt-9 as above, with the
\begin_inset Quotes eld
\end_inset
final
\begin_inset Quotes erd
\end_inset
merge algo fully implemented and
\begin_inset Quotes eld
\end_inset
debugged
\begin_inset Quotes erd
\end_inset
, started a long-running merge sometime in Oct, Nov and back-burnered it,
kicking it along every now and then, monitoring progress.
Now its time to examine it and see what we got.
\end_layout
\begin_layout Standard
Some stats:
\end_layout
\begin_layout Itemize
Starting dataset was `
\family sans
run-1-t1234-tsup-1-1-1.rdb
\family default
`.
This is copied to `
\family sans
run-1-t1234-shape.rdb
\family default
` and shapes are added.
This is copied to `
\family sans
r9-sim-200.rdb
\family default
` and the first 200x200 similarities are precomputed.
This is copied to `
\family sans
r9-merge-h.rdb
\family default
` and similarities start being computed.
\end_layout
\begin_layout Itemize
Data file: `
\family sans
r9-merge-h.rdb
\family default
` there's also an earlier one with about 2/3rds the total merges: `
\family sans
r9-merge-h-save1.rdb
\family default
`
\end_layout
\begin_layout Itemize
As above, parameters were quorum=0.5, commonality=20% and noise-floor = 4.
AKA `
\family sans
(in-group-cluster covr-obj 0.5 0.2 4 200 100)
\family default
` in the current code-base per late-Oct mid-Nov git repo contents.
This command was run maybe 20 or 30 times (??) by hand; each run was maybe
12 hours (??), I'd scan it, look for obvious failures (there weren't any),
and then run it again.
Each run picked up where the last left off, and would run deeper.
\end_layout
\begin_layout Itemize
18977 minutes total CPU (= 316 hours = 13 days) Of this time, 1988 minutes
spent in gc, or about 10.5%.
\end_layout
\begin_layout Itemize
126 GB RAM resident (this grew slowly).
The guile heap size is 7GB of which 6.7GB is free, so 387 MB in actual use.
The RAM blowup is due to pattern queries not being erased.
(See below)
\end_layout
\begin_layout Itemize
Total of 124820805 atoms (thats 125M).
RAM is 131717108 KB so thats 1.05KB/Atom so that's utterly normal.
\end_layout
\begin_layout Itemize
Most of the atoms are search queries that were not deleted! So that's a
bug.
After deleting the junk, have 7129235 atoms (that's 7M), so very tolerable.
\end_layout
\begin_layout Itemize
5190946
\family sans
SimilarityLinks
\family default
, (that's more than 5M of them) so similarities between approx 3222 words.
\end_layout
\begin_layout Itemize
4467
\family sans
MemberLinks
\family default
and 1393
\family sans
WordClassNodes
\family default
.
\end_layout
\begin_layout Standard
General impressions: Glancing at output during run, can see just a handful
of disjuncts being peeled of each word, and getting merged.
Often just one percent.
Sometimes see merges where 2/3rds of the disjunct of one word are merged
with just a few percent of the other words.
Neither word class seems to be very desirable.
\end_layout
\begin_layout Standard
The last few dozen merges were ...
curious.
They were:
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="14" columns="2">
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<column alignment="center" valignment="top">
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merged class
\end_layout
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Comments
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\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
line series
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
synonyms
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
S Ap
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
stray markup ?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
$ 1.00
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
tables?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
P 1.00
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
stray markup ?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1 1.00 B
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
numbers
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1.50 1
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
numbers
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
† 12mo
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
tables?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
\backslash
"that --
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
garbage punctuation
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
S Ag O
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Periodic table?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
S R C 2
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
tables?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
S 1 4
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
S No W
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
compass rose points?
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Leewit captain
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
fiction character title?
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
So these are not bad, but involve a lot of undue attention on stray markup.
For the 'line series' merge, the print says:
\end_layout
\begin_layout Standard
\begin_inset listings
inline false
status open
\begin_layout Plain Layout
In-group size=2 overlap = 1 of 87 disjuncts, commonality= 1.15%
\end_layout
\begin_layout Plain Layout
------ Assign: Merged 3 of 73 sections on `line` in 0.0 secs
\end_layout
\begin_layout Plain Layout
------ Assign: Merged 1 of 17 sections on `series` in 1.0 secs
\end_layout
\end_inset
So although 'line series' seems like a reasonable pair of synonyms, just
a small handful of sections are being peeled off of each one.
The 'Leewit captain' situation is a little better:
\begin_inset listings
inline false
status open
\begin_layout Plain Layout
In-group size=2 overlap = 3 of 37 disjuncts, commonality= 8.11%
\end_layout
\begin_layout Plain Layout
------ Assign: Merged 19 of 25 sections on `Leewit` in 0.0 secs
\end_layout
\begin_layout Plain Layout
------ Assign: Merged 3 of 31 sections on `captain` in 0.0 secs
\end_layout
\end_inset
This has the
\begin_inset Quotes eld
\end_inset
unbalanced
\begin_inset Quotes erd
\end_inset
feel to it: most of 'Leewit' gets merged into a handful of sections on
'captain', so that's not very impressive.
\end_layout
\begin_layout Subsection*
Things worth exploring.
\end_layout
\begin_layout Standard
Great.
So what have we actually got? Some questions about the dataset:
\end_layout
\begin_layout Itemize
Distribution: size of word-class vs.
rank.
This was previously examined in
\begin_inset Quotes eld
\end_inset
diary part one
\begin_inset Quotes erd
\end_inset
, page 99, for a different collection of merge algorithms (and earlier,
different datasets).
Do we still get something similar?
\end_layout
\begin_layout Itemize
Above,
\begin_inset Quotes eld
\end_inset
size
\begin_inset Quotes erd
\end_inset
might mean
\begin_inset Quotes eld
\end_inset
number of words in the word-class
\begin_inset Quotes erd
\end_inset
or it might mean
\begin_inset Quotes eld
\end_inset
number of disjuncts in word-class
\begin_inset Quotes erd
\end_inset
or it might mean
\begin_inset Quotes eld
\end_inset
number of disjuncts in word-class with count weighting
\begin_inset Quotes erd
\end_inset
.
Oof.
It would be nice to have a dashboard for this, instead of lots of manual
work.
\end_layout
\begin_layout Itemize
Distribution of word-senses.
That is, how many words participate in more than one word-class? If they
do participate in more than one word-class, what is the weight in each
class?
\end_layout
\begin_layout Itemize
For words that belong to word-classes, what fraction of their weight remains
unassigned to any word-class?
\end_layout
\begin_layout Itemize
Distribution of MI of pairs of word-classes.
We might hope that this is low, so that different word-classes are different
from one another.
\end_layout
\begin_layout Itemize
Distribution of self-MI of word-classes.
One might hope that this is high, so that the word-classes do not share
much in common with other words or word-classes.
\end_layout
\begin_layout Itemize
As above, but distribution of MI of pairs consisting of a word-class, and
a word.
\end_layout
\begin_layout Itemize
Prior to starting the merge, there's an MI between words and disjuncts.
I don't recall examining that in detail, before.
Then, after the merge, how does this change?
\end_layout
\begin_layout Standard
That's a lot of questions.
Not clear which ones should be answered first.
\end_layout
\begin_layout Subsection*
Issues with the dataset
\end_layout
\begin_layout Standard
There are problems.
Upon halt and reload of the dataset, the left-right partial sums are not
balanced.
Total counts are off by a factor of two.
This is a bug.
Is it serious?
\end_layout
\begin_layout Itemize
Starting dataset was `
\family sans
run-1-t1234-tsup-1-1-1.rdb
\family default
`.
\end_layout
\begin_layout Standard
From diary part three, page 6, we had this as the starting point:
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="7">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
filename
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
nwords
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ndisjuncts
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
total pairs
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
sparsity
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
obs/pair
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $MM^{T}$
\end_inset
ent
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
run-1-t1234-tsup-1-1-1
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
15083
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
205003
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
855718
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
11.819
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8.5462
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
16.352
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
The above is without shapes.
With shapes, it was:
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\family sans
run-1-t1234-tsup-1-1-1
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\family sans
run-1-t1234-shape
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
nwords
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
15083
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
15083
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ndisjuncts
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
205003
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1043583
\end_layout
\end_inset
</cell>
</row>
<row>
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\begin_inset Text
\begin_layout Plain Layout
total pairs
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
855718
\end_layout
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2777968
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
sparsity
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
11.819
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
12.468
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
total obs
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
22942644
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
obs/pair
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8.5462
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8.2588
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $MM^{T}$
\end_inset
ent
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
16.352
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
18.222
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
But the file `
\family sans
r9-merge-h.rdb
\family default
` shows
\end_layout
\begin_layout Standard
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="7">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
filename
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
nwords
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
ndisjuncts
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
total pairs
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
sparsity
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
obs/pair
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $MM^{T}$
\end_inset
ent
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
r9-merge-h
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
16452
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1110708
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
?
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
14.491
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
20.836
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
18.246
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
The following differences are notable:
\end_layout
\begin_layout Itemize
This shows 16452-15083=1369 which is almost but not quite the number of
word classes, so wtf?
\end_layout
\begin_layout Itemize
The number of disjuncts is 1110708 - 1043583 = 67125 more of them.
Seems plausible.
\end_layout
\begin_layout Itemize
The reported pair count is inconsistent: 793550.0 817444.0
\end_layout
\begin_layout Itemize
Sparsity is about the same as the pre-merge value.
\end_layout
\begin_layout Itemize
Observations per pair is probably just wrong.
\end_layout
\begin_layout Standard
How does one recompute the reported stats, again? ...
by running `
\family sans
marginals-mst-shape.scm
\family default
` aka `
\family sans
run/3-mst-parsing/compute-mst-marginals.sh
\family default
`
\end_layout
\begin_layout Section*
Expt-10 Merge exploration (Dec 2021)
\end_layout
\begin_layout Standard
The above generated a lot of confusion ...
A number of bugs were found and fixed in the merge code, and debugging
continues.
Once everything seems fully debugged and stable, analysis of merge results
will resume in the next part of the diary.
\end_layout
\begin_layout Standard
I did try restarting by copying `
\family sans
run-1-t1234-tsup-1-1-1.rdb
\family default
` and recomputing marginals.
This solved nothing; the marginals (and the similarities) appear to be
fine.
I'm currently using `
\family sans
r9-sim-200.rdb
\family default
` for marginals plus the similarities for the top 200 most frequent words.
\end_layout
\begin_layout Section*
Objdump (Dec 2021)
\end_layout
\begin_layout Standard
And now for something
\emph on
completely
\emph default
different.
So, this is a learning system.
It should be able to learn
\begin_inset Quotes eld
\end_inset
anything
\begin_inset Quotes erd
\end_inset
.
This section describes a wild-n-crazy idea of pumping disassembly through
the system.
Just to see what will happen.
This might seem irrational, and I don't have any great hopes for it, but
I'm curious to see ...
what will pop out.
\end_layout
\begin_layout Standard
We'll pump disassembled elf64 binaries through the system.
Disassembly to be done by
\family sans
objdump
\family default
.
It's cleaned up a bit with
\family sans
split-objdump.pl
\family default
in the
\family sans
run-common
\family default
directory.
Yes, one could develop a very sophisticated graph of the control flow.
This won't be done, as the short-term goal here is to see what's possible
with very little effort, instead of building in complex
\emph on
a priori
\emph default
knowledge about what assembly is.
\end_layout
\begin_layout Section*
The End
\end_layout
\begin_layout Standard
This is the end of Part Four of the diary.
The next part is Part Five.
\end_layout
\end_body
\end_document