Distributional Semantics in R with the ‘wordspace’ Package

Input formats

The most general representation of a distributional model takes the form of a sparse matrix, with entries specified as a triplet of row label (target term), column label (feature term) and co-occurrence frequency. A sample of such a table is included in the package under the name DSM_VerbNounTriples_BNC, listing syntactic verb-noun co-occurrences in the British National Corpus:

The wordspace package creates DSM objects from such triplet representations, which can easily be imported into R from a wide range of file and database formats. Ready-made import functions are provided for TAB-delimited text files (as used by DISSECT), which may be compressed to save disk space, and for term-document models created by the text-mining package tm.

The native input format is a pre-compiled sparse matrix representation generated by the UCS toolkit. In this way, UCS serves as a hub for the preparation of co-occurrence data, which can be collected from dependency pairs, extracted from a corpus indexed with the IMS Corpus Workbench or imported from various other formats.

Creating a DSM

The first step in the creation of a distributional semantic model is the compilation of a co-occurrence matrix. Let us illustrate the procedure for verb-noun co-occurrences from the written part of the British National Corpus. First, we extract relevant rows from the table above.

Triples <- subset(DSM_VerbNounTriples_BNC, mode == "written")

Note that many verb-noun pairs such as (walk, dog) still have multiple entries in Triples: dog can appear either as the subject or as the object of walk.

subset(Triples, noun == "dog" & verb == "walk")

##         noun  rel verb  f    mode
## 295011   dog subj walk 20 written
## 1398669  dog  obj walk 87 written

There are two ways of dealing with such cases: we can either add up the frequency counts (a dependency-filtered model) or treat “dog-as-subject” and “dog-as-object” as two different terms (a dependency-structured model). We opt for a dependency-filtered model in this example – can you work out how to compile the corresponding dependency-structured DSM in R, either for verbs of for nouns as target terms?

The dsm constructor function expects three vectors of the same length, containing row label (target term), column label (feature term) and co-occurrence count (or pre-weighted score) for each nonzero cell of the co-occurrence matrix. In our example, we use nouns as targets and verbs as features. Note the option raw.freq=TRUE to indicate that the matrix contains raw frequency counts.

VObj <- dsm(target=Triples$noun, feature=Triples$verb, score=Triples$f, raw.freq=TRUE)
dim(VObj)

## [1] 10940  3149

The constructor automatically computes marginal frequencies for the target and feature terms by summing over rows and columns of the matrix respectively. The information is collected in data frames VObj$rows and VObj$cols, together with the number of nonzero elements in each row and column:

subset(VObj$rows, rank(-f) <= 6) # 6 most frequent nouns

##         term nnzero     f
## 5395     man    907 51976
## 6491  people    911 72832
## 6951 problem    402 29002
## 8928   thing    442 34104
## 8975    time    658 46500
## 9613     way    738 46088

This way of computing marginal frequencies is appropriate for syntactic co-occurrence and term-document models. In the case of surface co-occurrence based on token spans, the correct marginal frequencies have to be provided separately in the rowinfo= and colinfo= arguments (see ?dsm for details).

The actual co-occurrence matrix is stored in VObj$M. Since it is too large to display on screen, we extract the top left corner with the head method for DSM objects. Note that you can also use head(VObj, Inf) to extract the full matrix.

head(VObj)

## 6 x 6 sparse Matrix of class "dgCMatrix"
##              be have say give take achieve
## aa            7    5  12    .    .       .
## abandonment  14    .   .    .    .       .
## abbey        45   13   6    .    .       .
## abbot        23    7  10    5    5       .
## abbreviation  9    .   .    .    .       .
## abc           6    .   .    .    .       .

The DSM parameters

Rows and columns with few nonzero cells provide unreliable semantic information and can lead to numerical problems (e.g. because a sparse association score deletes the remaining nonzero entries). It is therefore common to apply frequency thresholds both on rows and columns, here in the form of requiring at least 3 nonzero cells. The option recursive=TRUE guarantees that both criteria are satisfied by the final DSM when rows and columns are filtered at the same time (see the examples in ?subset.dsm for an illustration).

VObj <- subset(VObj, nnzero >= 3, nnzero >= 3, recursive=TRUE)
dim(VObj)

## [1] 6087 2139

If you want to filter only columns or rows, you can pass the constraint as a named argument: subset=(nnzero >= 3) for rows and select=(nnzero >= 3) for columns.

The next step is to weight co-occurrence frequency counts. Here, we use the simple log-likelihood association measure with an additional logarithmic transformation, which has shown good results in evaluation studies. The wordspace package computes sparse (or “positive”) versions of all association measures by default, setting negative associations to zero. This guarantees that the sparseness of the co-occurrence matrix is preserved. We also normalize the weighted row vectors to unit Euclidean length (normalize=TRUE).

VObj <- dsm.score(VObj, score="simple-ll", transform="log", normalize=TRUE, method="euclidean")

Printing a DSM object shows information about the dimensions of the co-occurrence matrix and whether it has already been scored. Note that the scored matrix does not replace the original co-occurrence counts, so dsm.score can be executed again at any time with different parameters.

VObj

## Distributional Semantic Model with 6087 rows x 2139 columns
## * raw co-occurrence matrix M available
##   - sparse matrix with 191.4k / 13.0M nonzero entries (fill rate = 1.47%)
##   - in canonical format
##   - known to be non-negative
##   - sample size of underlying corpus: 5010.1k tokens
## * scored matrix S available
##   - sparse matrix with 153.7k / 13.0M nonzero entries (fill rate = 1.18%)
##   - in canonical format
##   - known to be non-negative

Most distributional models apply a dimensionality reduction technique to make data sets more manageable and to refine the semantic representations. A widely-used technique is singular value decomposition (SVD). Since VObj is a sparse matrix, dsm.projection automatically applies an efficient algorithm from the sparsesvd package.

VObj300 <- dsm.projection(VObj, method="svd", n=300)
dim(VObj300)

## [1] 6087  300

VObj300 is a dense matrix with 300 columns, giving the coordinates of the target terms in 300 latent dimensions. Its attribute "R2" shows what proportion of information from the original matrix is captured by each latent dimension.

plot(attr(VObj300, "R2"), type="h", xlab="latent dimension", ylab="R2")

Using DSM representations

The primary goal of a DSM is to determine “semantic” distances between pairs of words. The arguments to pair.distances can also be parallel vectors in order to compute distances for a large number of word pairs efficiently.

pair.distances("book", "paper", VObj300, method="cosine")

## book/paper 
##   45.07627 
## attr(,"similarity")
## [1] FALSE

By default, the function converts similarity measures into an equivalent distance metric – the angle between vectors in the case of cosine similarity. If you want the actual similarity values, specify convert=FALSE:

pair.distances("book", "paper", VObj300, method="cosine", convert=FALSE)

## book/paper 
##  0.7061649 
## attr(,"similarity")
## [1] TRUE

We are often interested in finding the nearest neighbours of a given term in the DSM space:

nearest.neighbours(VObj300, "book", n=14) # reduced space

##     paper   article      poem     works  magazine     novel      text     guide 
##  45.07627  51.92011  53.48027  53.91556  53.94824  54.40451  55.13910  55.27027 
## newspaper  document      item     essay   leaflet    letter 
##  55.51492  55.62521  56.28246  56.29539  56.49145  58.04178

The return value is actually a vector of distances to the nearest neighbours, labelled with the corresponding terms. Here is how you obtain the actual neighbour terms:

nn <- nearest.neighbours(VObj, "book", n=15)    # unreduced space
names(nn)

##  [1] "paper"     "guide"     "works"     "novel"     "magazine"  "article"  
##  [7] "document"  "poem"      "diary"     "essay"     "item"      "text"     
## [13] "booklet"   "leaflet"   "newspaper"

The neighbourhood plot visualizes nearest neighbours as a semantic network based on their mutual distances. This often helps interpretation by grouping related neighbours. The network below shows that book as a text type is similar to novel, essay, poem and article; as a form of document it is similar to paper, letter and document; and as a publication it is similar to leaflet, magazine and newspaper.

nn.mat <- nearest.neighbours(VObj300, "book", n=15, dist.matrix=TRUE)
plot(nn.mat)

A straightforward way to evaluat distributional representations is to compare them with human judgements of the semantic similarity between word pairs. The wordspace package includes to well-known data sets of this type: Rubenstein-Goodenough (RG65) and WordSim353 (a superset of RG65 with judgements from new test subjects).

There is also a ready-made evaluation function, which computes Pearson and rank correlation between the DSM distances and human subjects. The option format="HW" adjusts the POS-disambiguated notation for terms in the data set (e.g. book_N) to the format used by our distributional model (book).

eval.similarity.correlation(RG65, VObj300, convert=FALSE, format="HW")

##            rho    p.value missing         r   r.lower   r.upper
## RG65 0.3076154 0.01267694      20 0.3735435 0.1426399 0.5658865

Evaluation results can also be visualized in the form of a scatterplot with a trend line.

plot(eval.similarity.correlation(RG65, VObj300, convert=FALSE, format="HW", details=TRUE))

The rank correlation of 0.308 is very poor, mostly due to the small amount of data on which our DSM is based. Much better results are obtained with pre-compiled DSM vectors from large Web corpus, which are also included in the package. Note that target terms are given in a different format there (which corresponds to the format in RG65).

plot(eval.similarity.correlation(RG65, DSM_Vectors, convert=FALSE, details=TRUE))

Advanced techniques

Schütze (1998) used DSM representations for word sense disambiguation (or, more precisely, word sense induction) based on a clustering of the sentence contexts of an ambiguous word. The wordspace package includes a small data set with such contexts for a selection of English words. Let us look at the noun vessel as an example, which has two main senses (“ship” and “blood vessel”):

Vessel <- subset(SemCorWSD, target == "vessel" & pos == "n")
table(Vessel$gloss)

## 
## a craft designed for water transportation 
##                                         6 
##   a tube in which a body fluid circulates 
##                                         6

Sentence contexts are given as tokenized strings ($sentence), in lemmatized form ($hw) and as lemmas annotated with part-of-speech codes ($lemma). Choose the version that matches the representation of target terms in your DSM.

Following Schütze, each context is represented by a centroid vector obtained by averaging over the DSM vectors of all context words.

centroids <- context.vectors(DSM_Vectors, Vessel$lemma, row.names=Vessel$id)

This returns a matrix of centroid vectors for the 12 sentence contexts of vessel in the data set. The vectors can now be clustered and analyzed using standard R functions. Partitioning around medoids (PAM) has shown good and robust performance in evaluation studies.

library(cluster) # clustering algorithms of Kaufman & Rousseeuw (1990)
res <- pam(dist.matrix(centroids), 2, diss=TRUE, keep.diss=TRUE)
plot(res, col.p=factor(Vessel$sense), shade=TRUE, which=1, main="WSD for 'vessel'")

Colours in the plot above indicate the gold standard sense of each instance of vessel. A confusion matrix confirms perfect clustering of the two senses:

## table(res$clustering, Vessel$sense)

We can also use a pre-defined function for the evaluation of clustering tasks, which is convenient but does not produce a visualization of the clusters. Note that the “target terms” of the task must correspond to the row labels of the centroid matrix, which we have set to sentence IDs (Vessel$id) above.

eval.clustering(Vessel, M=centroids, word.name="id", class.name="sense")

##        purity entropy missing
## Vessel    100       0       0

As a final example, let us look at a simple approach to compositional distributional semantics, which computes the compositional meaning of two words as the element-wise sum or product of their DSM vectors.

mouse <- VObj300["mouse", ] # extract row vectors from matrix
computer <- VObj300["computer", ]

The nearest neighbours of mouse are problematic, presumably because the type vector represents a mixture of the two senses that is not close to either meaning in the semantic space.

nearest.neighbours(VObj300, "mouse", n=12)

##        prop     isotope      carbon       serum transformer      sponge 
##    53.72837    55.08473    55.29022    56.84607    57.20004    57.25144 
## thermometer        hoop loudspeaker       razor       mount     implant 
##    57.33371    57.38682    57.38682    57.43123    57.47889    57.49171

By adding the vectors of mouse and computer, we obtain neighbours that seem to fit the “computer mouse” sense very well:

nearest.neighbours(VObj300, mouse + computer, n=12)

##      mouse   computer    program  processor   software       tool    machine 
##   36.69755   41.47028   54.15183   54.37412   54.55897   55.07898   55.74764 
## transistor        mix   keyboard       prop     sponge 
##   58.51586   58.93807   59.15682   59.18378   59.34185

Note that the target is specified as a distributional vector rather than a term in this case. Observations from the recent literature suggest that element-wise multiplication is not compatible with non-sparse SVD-reduced DSMs, so it is not surprising to find completely unrelated nearest neighbours in our example:

nearest.neighbours(VObj300, mouse * computer, n=12)

##     kylie     barry    coward       leo wednesday      emma     baron     leech 
##  52.70435  52.92230  53.61260  53.81451  54.01588  54.33543  54.53792  55.07008 
##    friday     frank   colonel     bruce 
##  55.28301  55.39203  55.44021  55.47596