1. Text embeddings

Thomas W. Jones

2018-09-10

Text embeddings

Text embeddings are particularly hot right now. While textmineR doesn’t (yet) explicitly implement any embedding models like GloVe or word2vec, you can still get embeddings. Text embedding algorithms aren’t conceptually different from topic models. They are, however, operating on a different matrix. Instead of reducing the dimensions of a document term matrix, text embeddings are obtained by reducing the dimensions of a term co-occurrence matrix. In principle, one can use LDA or LSA in the same way. In this case, rows of theta are embedded words. A phi_prime may be obtained to project documents or new text into the embedding space.

Create a term co-occurrence matrix

The first step in fitting a text embedding model is to create a term co-occurrence matrix or TCM. In a TCM, both columns and rows index tokens. The \((i,j)\) entries of the matrix are a count of the number of times word \(i\) co-occures with \(j\). However, there are several ways to count co-occurrence. textmineR gives you three.

The most useful way of counting co-occurrence for text embeddings is called the skip-gram model. Under the skip-gram model, the count would be the number of times word \(j\) appears within a certain window of \(i\). A skip-gram window of two, for example, would count the number of times word \(j\) occured in the two words immediately before word \(i\) or the two words immediately after word \(i\). This helps capture the local context of words. In fact, you can think of a text embedding as being a topic model based on the local context of words. Whereas a traditional topic model is modeling words in their global context.

To read more about the skip-gram model, which was popularized in the embedding model word2vec, look here.

The other types of co-occurence matrix textmineR provides are both global. One is a count of the number of documents in which words \(i\) and \(j\) co-occur. The other is the number of terms that co-occur between documents \(i\) and \(j\). See help(CreateTcm) for info on these.


# load the NIH data set
library(textmineR)

# load nih_sample data set from textmineR
data(nih_sample)

# First create a TCM using skip grams, we'll use a 5-word window
# most options available on CreateDtm are also available for CreateTcm
tcm <- CreateTcm(doc_vec = nih_sample$ABSTRACT_TEXT,
                 skipgram_window = 5,
                 verbose = FALSE,
                 cpus = 2)

# a TCM is generally larger than a DTM
dim(tcm)
#> [1] 5210 5210

Fitting a model

Once we have a TCM, we can use the same procedure to make an embedding model as we used to make a topic model. Note that it may take considerably longer (because of dimensionality of the matrix) or shorter (because of sparsity) to fit an embedding on the same corpus.

# use LDA to get embeddings into probability space
# This will take considerably longer as the TCM matrix has many more rows 
# than a DTM
embeddings <- FitLdaModel(dtm = tcm,
                          k = 100,
                          iterations = 200, # i recommend a larger value, 500 or more
                          cpus = 2)

Interpretation of \(\Phi\) and \(\Theta\)

In the language of text embeddings, \(\Theta\) gives us our tokens embedded in a probability space (because we used LDA, Euclidean space if we used LSA). \(\Phi\) defines the dimensions of our embbeding space. The rows of \(\Phi\) can still be interpreted as topics. But they are topics of local contexts, rather than within whole documents.

Evaluating the model

As it happens, the same evaluation metrics developed for topic modeling also apply here. There are subtle differences in interpretation because we are using a TCM not a DTM. i.e. occurrences relate words to each other, not to documents.

# Get an R-squared for general goodness of fit
embeddings$r2 <- CalcTopicModelR2(dtm = tcm, 
                                  phi = embeddings$phi,
                                  theta = embeddings$theta,
                                  cpus = 2)

embeddings$r2
#> [1] 0.2786783

# Get coherence (relative to the TCM) for goodness of fit
embeddings$coherence <- CalcProbCoherence(phi = embeddings$phi,
                                          dtm = tcm)

summary(embeddings$coherence)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> -0.005319  0.014635  0.045040  0.058624  0.092362  0.189357

We will create a summary table as we did with a topic model before.

# Get top terms, no labels because we don't have bigrams
embeddings$top_terms <- GetTopTerms(phi = embeddings$phi,
                                    M = 5)
# Create a summary table, similar to the above
embeddings$summary <- data.frame(topic = rownames(embeddings$phi),
                                 coherence = round(embeddings$coherence, 3),
                                 prevalence = round(colSums(embeddings$theta), 2),
                                 top_terms = apply(embeddings$top_terms, 2, function(x){
                                   paste(x, collapse = ", ")
                                 }),
                                 stringsAsFactors = FALSE)

Here it is ordered by prevalence. (Here, we might say density of tokens along each embedding dimension.)

embeddings$summary[ order(embeddings$summary$prevalence, decreasing = TRUE) , ][ 1:10 , ]
Summary of top 10 embedding dimensions
topic coherence prevalence top_terms
t_80 t_80 0.166 126.94 aim, study, research, specific, studies
t_60 t_60 0.129 109.13 research, program, support, training, investigators
t_28 t_28 0.127 106.72 cells, cell, human, brain, tissue
t_27 t_27 0.154 99.38 health, research, clinical, treatment, cancer
t_81 t_81 0.077 78.59 data, studies, work, results, methods
t_12 t_12 0.076 68.72 hiv, based, secondary, effective, design
t_92 t_92 0.133 66.98 mechanisms, role, genetic, gene, specific
t_54 t_54 0.162 65.62 dependent, sleep, memory, cellular, cognitive
t_87 t_87 0.107 63.25 factors, risk, function, sud, social
t_17 t_17 0.065 61.90 large, wall, structural, understand, arterial

And here is the table ordered by coherence.

embeddings$summary[ order(embeddings$summary$coherence, decreasing = TRUE) , ][ 1:10 , ]
Summary of 10 most coherent embedding dimensions
topic coherence prevalence top_terms
t_18 t_18 0.189 45.51 acids, fertility, ethnic, race, differences
t_80 t_80 0.166 126.94 aim, study, research, specific, studies
t_54 t_54 0.162 65.62 dependent, sleep, memory, cellular, cognitive
t_64 t_64 0.162 60.58 microbiome, gut, composition, crc, tract
t_27 t_27 0.154 99.38 health, research, clinical, treatment, cancer
t_55 t_55 0.149 44.89 long, term, goal, da, aim
t_84 t_84 0.146 49.40 pathways, carbon, information, intracellular, define
t_47 t_47 0.136 48.71 influenza, vaccine, strain, induced, antigen
t_92 t_92 0.133 66.98 mechanisms, role, genetic, gene, specific
t_20 t_20 0.130 50.50 blood, release, fragment, determine, important

Embedding documents under the model

You can embed whole documents under your model. Doing so, effectively makes your embeddings a topic model that have topics of local contexts, instead of global ones. Why might you want to do this? The short answer is that you may have reason to believe that an embedding model may give you better topics, especially if you are trying to pick up on more subtle topics. In a later example, we’ll be doing that to build a document summarizer.

# Make a DTM from our documents
dtm_embed <- CreateDtm(doc_vec = nih_sample$ABSTRACT_TEXT,
                       doc_names = nih_sample$APPLICATION_ID,
                       ngram_window = c(1,1),
                       verbose = FALSE,
                       cpus = 2)

dtm_embed <- dtm_embed[ , colnames(tcm) ] # make sure vocab lines up

# Get phi_prime, the projection matrix
embeddings$phi_prime <- CalcPhiPrime(phi = embeddings$phi,
                                     theta = embeddings$theta)

# Project the documents into the embedding space
embedding_assignments <- dtm_embed / rowSums(dtm_embed)

embedding_assignments <- embedding_assignments %*% t(embeddings$phi_prime)

embedding_assignments <- as.matrix(embedding_assignments)

Once you’ve embedded your documents, you effectively have a new \(\Theta\). We can use that to evaluate how well the embedding topics fit the documents as a whole by re-calculaing R-squared and coherence.

# get a goodness of fit relative to the DTM
embeddings$r2_dtm <- CalcTopicModelR2(dtm = dtm_embed, 
                                      phi = embeddings$phi,
                                      theta = embedding_assignments,
                                      cpus = 2)

embeddings$r2_dtm
#> [1] 0.1632364

# get coherence relative to DTM
embeddings$coherence_dtm <- CalcProbCoherence(phi = embeddings$phi,
                                              dtm = dtm_embed)

summary(embeddings$coherence_dtm)
#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#> -0.07839  0.01444  0.05425  0.08502  0.12789  0.44900

Where to next?

Embedding research is only just beginning. I would encourage you to play with them and develop your own methods.