Topic modeling is technique to extract abstract topics from a collection of documents. In order to do that input Document-Term matrix usually decomposed into 2 low-rank matrices: document-topic matrix and topic-word matrix.

# Latent Semantic Analysis

Latent Semantic Analysis is the oldest among topic modeling techniques. It decomposes Document-Term matrix into a product of 2 low rank matrices $$X \approx D \times T$$. Goal of LSA is to receive approximation with a respect to minimize Frobenious norm: $$error = \left\lVert X - D \times T \right\rVert _F$$. Turns out this can be done with truncated SVD decomposition.

text2vec borrows SVD from very efficient irlba package and adds convenient interface with an ability to fit model and apply it to new data.

## Example

As usual we will use built-in text2vec::moview_review dataset. Let’s clean it a bit and create DTM:

library(stringr)
library(text2vec)
data("movie_review")
# select 1000 rows for faster running times
movie_review_train = movie_review[1:700, ]
movie_review_test = movie_review[701:1000, ]
prep_fun = function(x) {
x %>%
# make text lower case
str_to_lower %>%
# remove non-alphanumeric symbols
str_replace_all("[^[:alpha:]]", " ") %>%
# collapse multiple spaces
str_replace_all("\\s+", " ")
}
movie_review_train$review = prep_fun(movie_review_train$review)
it = itoken(movie_review_train$review, progressbar = FALSE) v = create_vocabulary(it) %>% prune_vocabulary(doc_proportion_max = 0.1, term_count_min = 5) vectorizer = vocab_vectorizer(v) dtm = create_dtm(it, vectorizer) Now we will perform tf-idf scaling and fit LSA model: tfidf = TfIdf$new()
lsa = LSA$new(n_topics = 10) # pipe friendly transformation doc_embeddings = dtm %>% fit_transform(tfidf) %>% fit_transform(lsa) doc_embeddings contains matrix with document embeddings (document-topic matrix) and lsa$components contains topic-word matrix:

dim(doc_embeddings)
## [1] 700  10
dim(lsa$components) ## [1] 10 3029 Usually we need not only analyze a fixed dataset, but also apply model to new data. For instance we may need to embed unseen documents into the same latent space in order to use their representation in some downstream task (for example classification). text2vec keep in mind such task from the very first days of development. We can elegantly perform exactly the same transformation on the new data with transform() method and “not-a-pipe” %>%: new_data = movie_review_test new_doc_embeddings = new_data$review %>%
itoken(preprocessor = prep_fun, progressbar = FALSE) %>%
create_dtm(vectorizer) %>%
# apply exaxtly same scaling wcich was used in train data
transform(tfidf) %>%
# embed into same space as was in train data
transform(lsa)
dim(new_doc_embeddings)
## [1] 300  10

## Pros and cons

Pros:

1. LSA is easy to train and tune (no hyperparameters except rank)
2. Embeddings usually work fine in dowstream tasks such as clusterization, classification, regression, similarity-search

Cons:

1. Major drawback is that embeddings are not interpretable (components might be negative)
2. Could be quite slow to train on very large collections of documents
3. The probabilistic model of LSA does not match observed data: LSA assumes that words and documents form a joint Gaussian model (ergodic hypothesis), while a Poisson distribution has been observed

# Latent Dirichlet Allocation

LDA (Latent Dirichlet Allocation) model also decomposes document-term matrix into two low-rank matrices - document-topic distribution and topic-word distribution. Bit it is more complex non-linear generative model. We won’t go into gory details behind LDA probabilistic model, reader can find a lot of material on the internet. For example wikipedia article is pretty good. We will rather focus on practical details.

There several important hyper-parameters:

1. n_topics - Number of latent topics.
2. doc_topic_prior - document-topic prior. Normally a number less than 1, e.g. 0.1, to prefer sparse topic distributions, i.e. few topics per document.
3. topic_word_prior - topic-word prior. Normally a number much less than 1, e.g. 0.001, to strongly prefer sparse word distributions, i.e. few words per topic.

LDA in text2vec is implemented using iterative sampling algorithm - it improves log-likelihood with every pass over the data. So user can set convergence_tol parameter for early stopping - algorithm will stop iteration if improvement is not significant. For example setting lda$fit_transform(x, n_iter = 1000, convergence_tol = 1e-3, n_check_convergence = 10) will stop earlier if log-likelihood at iteration n is within 0.1% of the log-likelihood of iteration n - 10. ### Remark on implementation text2vec implementation is based on the state-of-the-art WarpLDA sampling algorithm. It has O(1) sampling complexity which means run-time does not depend on the number of topics. Current implementation is single-threaded and reasonably fast. However it can be improved in future versions. ### Example Let us create topic model with 10 topics: tokens = movie_review$review[1:4000] %>%
tolower %>%
word_tokenizer
it = itoken(tokens, ids = movie_review$id[1:4000], progressbar = FALSE) v = create_vocabulary(it) %>% prune_vocabulary(term_count_min = 10, doc_proportion_max = 0.2) vectorizer = vocab_vectorizer(v) dtm = create_dtm(it, vectorizer, type = "dgTMatrix") lda_model = LDA$new(n_topics = 10, doc_topic_prior = 0.1, topic_word_prior = 0.01)
doc_topic_distr =
lda_model$fit_transform(x = dtm, n_iter = 1000, convergence_tol = 0.001, n_check_convergence = 25, progressbar = FALSE) ## INFO [2017-07-12 09:28:41] iter 25 loglikelihood = -2739471.624 ## INFO [2017-07-12 09:28:42] iter 50 loglikelihood = -2689784.369 ## INFO [2017-07-12 09:28:43] iter 75 loglikelihood = -2665906.863 ## INFO [2017-07-12 09:28:44] iter 100 loglikelihood = -2650951.848 ## INFO [2017-07-12 09:28:45] iter 125 loglikelihood = -2640540.549 ## INFO [2017-07-12 09:28:46] iter 150 loglikelihood = -2631921.113 ## INFO [2017-07-12 09:28:47] iter 175 loglikelihood = -2625292.752 ## INFO [2017-07-12 09:28:48] iter 200 loglikelihood = -2622313.280 ## INFO [2017-07-12 09:28:49] iter 225 loglikelihood = -2617041.128 ## INFO [2017-07-12 09:28:50] iter 250 loglikelihood = -2614400.745 ## INFO [2017-07-12 09:28:51] iter 275 loglikelihood = -2612813.374 ## INFO [2017-07-12 09:28:51] early stopping at 275 iteration Now doc_topic_distr matrix represents distribution of topics in documents. Each row is document and values are proportions of corresponding topics. For example topic distribution for first document: barplot(doc_topic_distr[1, ], xlab = "topic", ylab = "proportion", ylim = c(0, 1), names.arg = 1:ncol(doc_topic_distr)) ## Describing topics - top words Also we can get top words for each topic. They can be sorted by probability of the chance to observe word in a given topic (lambda = 1): lda_model$get_top_words(n = 10, topic_number = c(1L, 5L, 10L), lambda = 1)
##       [,1]        [,2]     [,3]
##  [1,] "know"      "war"    "director"
##  [2,] "horror"    "before" "films"
##  [3,] "why"       "years"  "quite"
##  [4,] "your"      "still"  "while"
##  [5,] "worst"     "world"  "little"
##  [6,] "guy"       "man"    "horror"
##  [7,] "nothing"   "match"  "though"
##  [8,] "something" "best"   "such"
##  [9,] "scene"     "these"  "may"
## [10,] "ever"      "part"   "enough"

Also top-words could be sorted by “relevance” which also takes into account frequency of word in the corpus (0 < lambda < 1). From my experience in most cases setting 0.2 < lambda < 0.4 works best. See LDAvis: A method for visualizing and interpreting topics paper for details.

lda_model$get_top_words(n = 10, topic_number = c(1L, 5L, 10L), lambda = 0.2) ## [,1] [,2] [,3] ## [1,] "zombie" "war" "atmosphere" ## [2,] "gore" "match" "thriller" ## [3,] "stupid" "anti" "viewer" ## [4,] "cheesy" "army" "page" ## [5,] "flick" "green" "narrative" ## [6,] "horror" "jackson" "identity" ## [7,] "zombies" "hitler" "images" ## [8,] "slasher" "soldiers" "france" ## [9,] "killer" "historical" "engaging" ## [10,] "worst" "kelly" "caine" ## Apply learned model to new data As with other decompositions we can apply model to new data and obtain document-topic distribution: new_dtm = itoken(movie_review$review[4001:5000], tolower, word_tokenizer, ids = movie_review$id[4001:5000]) %>% create_dtm(vectorizer, type = "dgTMatrix") new_doc_topic_distr = lda_model$transform(new_dtm)
## INFO [2017-07-20 15:50:25] iter 5 loglikelihood = -509731.596
## INFO [2017-07-20 15:50:25] iter 10 loglikelihood = -504774.598
## INFO [2017-07-20 15:50:25] iter 15 loglikelihood = -504082.274
## INFO [2017-07-20 15:50:25] iter 20 loglikelihood = -503266.085
## INFO [2017-07-20 15:50:25] iter 25 loglikelihood = -503086.430
## INFO [2017-07-20 15:50:25] early stopping at 25 iteration

## Cross-validation and hyper-parameter tuning

One widely used approach for model hyper-parameter tuning is validation of per-word perplexity on hold-out set. This is quite easy with text2vec.

### Perplexity example

Remember that we’ve fitted model on first 4000 reviews (learned topic_word_distribution which will be fixed during transform phase) and predicted last 1000. We can calculate perplexity on these 1000 docs:

LDAvis