On the relation between K-means and PLSA

Non-negative matrix factorization
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(NMF) is a well known tool for unsupervised machine learning. It can be viewed as a generalization of the K-means clustering, Expectation Maximization based clustering and aspect modeling by Probabilistic Latent Semantic Analysis (PLSA). Specifically PLSA is related to NMF with KL-divergence objective function. Further it is shown that K-means clustering is a special case of NMF with matrix L2 norm based error function. In this paper our objective is to analyze the relation between K-means clustering and PLSA by examining the KL-divergence function and matrix L2 norm based error function.