Variational Extensions to EM and Multinomial PCA

Several authors in recent years have proposed discrete analogues to principle component analysis intended to handle discrete or positive only data, for instance suited to analyzing sets of documents. Methods include non-negative matrix factorization, probabilistic latent semantic analysis, and latent Dirichlet allocation. This paper% begins with a review of the basic theory of the variational extension to the expectation-maximization algorithm, and then presents discrete component finding algorithms in that light. Experiments are conducted on both bigram word data and document bag-of-word to expose some of the subtleties of this new class of algorithms.