On the equivalence between algorithms for non-negative matrix factorization and latent Dirichlet allocation

Abstract

LDA (Latent Dirichlet Allocation ) and NMF (Non-negative Matrix Factorization) are two popular techniques to extract topics in a textual document corpus. This paper shows that NMF with Kullback-Leibler divergence approximate the LDA model under a uniform Dirichlet prior, therefore the comparative analysis can be useful to elucidate the implementation of variational inference algorithm for LDA.