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In my previous post I used the tm package to do some simple text mining on the Complete Works of William Shakespeare. Today I am taking some of those results and using them to generate word clusters.

# Preparing the Data

I will start with the Term Document Matrix (TDM) consisting of 71 words commonly used by Shakespeare.

> inspect(TDM.common[1:10,1:10])
A term-document matrix (10 terms, 10 documents)

Non-/sparse entries: 94/6
Sparsity           : 6%
Maximal term length: 6
Weighting          : term frequency (tf)

Docs
Terms     1 2  3  4  5  6  7  8 9 10
act     1 4  7  9  6  3  2 14 1  0
art    53 0  9  3  5  3  2 17 0  6
away   18 5  8  4  2 10  5 13 1  7
call   17 1  4  2  2  1  6 17 3  7
can    44 8 12  5 10  6 10 24 1  5
come   19 9 16 17 12 15 14 89 9 15
day    43 2  2  4  1  5  3 17 2  3
enter   0 7 12 11 10 10 14 87 4  6
exeunt  0 3  8  8  5  4  7 49 1  4
exit    0 6  8  5  6  5  3 31 3  2


This matrix is first converted from a sparse data format into a conventional matrix.

> TDM.dense  dim(TDM.dense)
[1]  71 182


Next the TDM is normalised so that the rows sum to unity. Each entry in the normalised TDM then represents the number of times that a word occurs in a particular document relative to the number of occurrences across all of the documents.

> TDM.scaled

# Clustering

We will be using a hierarchical clustering technique which operates on a dissimilarity matrix. We will use the Euclidean distance between each of the rows in the TDM, where each row is treated as a vector in a space of 182 dimensions.

> TDM.dist = dist(TDM.scaled)


Finally we perform agglomerative clustering using agnes() from the cluster package.

> library(cluster)
>
> hclusters  hclusters
Call:	 agnes(x = TDM.dist, method = "complete")
Agglomerative coefficient:  0.6256247
Order of objects:
[1] act    great  way    away   hand   stand  life   can    hath   yet
[11] look   see    leav   let    shall  make   take   thus   made   till
[21] come   well   will   good   ill    like   now    give   upon   know
[31] may    must   man    much   think  hear   speak  never  one    say
[41] tell   enter  exeunt scene  exit   tis    mean   fear   men    keep
[51] word   name   lord   call   two    old    sir    first  art    thee
[61] thou   thi    day    live   heart  mine   time   part   true   eye
[71] love
Height (summary):
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.02495 0.04509 0.05722 0.06050 0.06897 0.14260

Available components:
[1] "order"     "height"    "ac"        "merge"     "diss"      "call"
[7] "method"    "order.lab"


# Plotting a Dendrogram

Let’s have a look at the results of our labours.

plot(hclusters, which.plots = 2, main = "", sub = "", xlab = "")


This dendrogram reflects the tree-like structure of the word clusters. We can see that the words “enter”, “exeunt” and “scene” are clustered together, which makes sense since they are related to stage directions. Also “thee” and “thou” have similar usage. In the previous analysis we found that the occurrences of “love” and “eye” were highly correlated and consequently we find them clustered here too.

This is rather cool. No doubt a similar analysis applied to contemporary literature would yield extremely different results. Anybody keen on clustering the Complete Works of Terry Pratchett?