Relation between PLSA and NMF and implications

Non-negative Matrix Factorization (NMF, 5) and Probabilistic Latent Semantic Analysis (PLSA, 4) have been successfully applied to a number of text analysis tasks such as document clustering. Despite their different inspirations, both methods are instances of multinomial PCA 1. We further explore this relationship and first show that PLSA solves the problem of NMF with KL divergence, and then explore the implications of this relationship.