Topic Modeling Based on Variational Bayes Method

The Latent Dirichlet Allocation (LDA) model is a generative model with several applications in natural language processing, text mining, dimension reduction, and bioinformatics. It is a powerful technique in topic modeling in text mining, which is a data mining method to categorize documents by their topic. Basic methods for topic modeling, including TF-IDF, unigram, and mixture of unigrams successfully deployed in modern search engines. Although these methods have some useful benefits, they don’t provide much summarization and reduction. To overcome these shortcomings, the latent semantic analysis (LSA) has been proposed, which uses singular value decomposition (SVD) of word-document matrix to compress big collection of text corpora. User’s search key words can be queried by making a pseudo-document vector. The next improvement step in topic modeling was probabilistic latent semantic analysis (PLSA), which has a close relation to LSA and matrix decomposition with SVD. By introducing of exchangeability for the words in documents, the topic modeling has been proceeded beyond PLSA and leads to LDA model. We consider a corpus  contains M  documents, each document  has  words, and each word is an indicator from one of  vocabularies. We defined a generative model for generation of each document as follows. For each document draw its topic  from  and repeatedly for each  draw topic of each word  from  and draw each word from the probability matrix of  with probability of . We can repeat this procedure to generate whole documents of corpus. We want to find corpus related parameters  and  as well as latent variables  and  for each document. Unfortunately, the posterior  is intractable, and we have to choose an approximation scheme. In this paper we utilize LDA for collection of discrete text corpora. We describe procedures for inference and parameter estimation. Since computing posterior distribution of hidden variables given a document is intractable to compute in general, we use approximate inference algorithm called variational Bayes method. The basic idea of variational Bayes is to consider a family of adjustable lower bound on the posterior, then finds the tightest possible one. To estimate optimal hyper-parameters in the model, we used the empirical Bayes method, as well as a specialized expectation-maximization (EM) algorithm called variational-EM algorithm. The results are reported in document modeling, text classification, and collaborative filtering. The topic modeling of LDA and PLSA models are compared on a Persian news data set. It has been observed that LDA has perplexity between  and , while the PLSA has perplexity between  and , which shows domination of LDA over PLSA. The LDA model has also been applied for dimension reduction in a document classification problem, along with the support vector machines (SVM) classification method. Two competitor models are compared, first trained on a low-dimensional representation provided by LDA and the second trained on all documents of corpus, with accuracies  and , respectively, this means we lose accuracy but it remains in reasonable range when we use LDA model for dimensionality reduction. Finally, we used the LDA and PLSA methods along with the collaborative filtering for MovieLens 1m data set, and we observed that the predictive-perplexity of LDA changes from  to  while it changes from  to  for PLSA, again showing the domination of the LDA method.