Probabilistic matrix tri-factorization

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Probabilistic matrix tri-factorization
Nonnegative matrix tri-factorization (NMTF) is a 3-factor decomposition of a nonnegative data matrix, X USV , where factor matrices, U, S, and V , are restricted to be nonnegative as well. Motivated by the aspect model used for dyadic data analysis as well as in probabilistic latent semantic analysis (PLSA), we present a probabilistic model with two dependent latent variables for NMTF, referred to as probabilistic matrix tri-factorization (PMTF). Each latent variable in the model is associated with the cluster variable for the corresponding object in the dyad, leading the model suited to coclustering. We develop an EM algorithm to learn the PMTF model, showing its equivalence to multiplicative updates derived by an algebraic approach. We demonstrate the useful behavior of PMTF in a task of document clustering. Moreover, we incorporate the likelihood in the PMTF model into existing information criteria so that the number of clusters can be detected, while the algebraic NMTF cannot.
Jiho Yoo, Seungjin Choi
Added 18 Feb 2011
Updated 18 Feb 2011
Type Journal
Year 2009
Authors Jiho Yoo, Seungjin Choi
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