Nonnegative tensor factorization as an alternative Csiszar---Tusnady procedure: algorithms, convergence, probabilistic interpretations and novel probabilistic tensor latent variable analysis algorithms

Authors:
Stefanos Zafeiriou;Maria Petrou
Affiliations:
Department of Electrical and Electronic Engineering, Imperial College London, Signal Processing and Communication Research Group, London, UK SW7 2AZ;Department of Electrical and Electronic Engineering, Imperial College London, Signal Processing and Communication Research Group, London, UK SW7 2AZ
Venue:
Data Mining and Knowledge Discovery
Year:
2011

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Abstract

In this paper we study Nonnegative Tensor Factorization (NTF) based on the Kullback---Leibler (KL) divergence as an alternative Csiszar---Tusnady procedure. We propose new update rules for the aforementioned divergence that are based on multiplicative update rules. The proposed algorithms are built on solid theoretical foundations that guarantee that the limit point of the iterative algorithm corresponds to a stationary solution of the optimization procedure. Moreover, we study the convergence properties of the optimization procedure and we present generalized pythagorean rules. Furthermore, we provide clear probabilistic interpretations of these algorithms. Finally, we discuss the connections between generalized Probabilistic Tensor Latent Variable Models (PTLVM) and NTF, proposing in that way algorithms for PTLVM for arbitrary multivariate probabilistic mass functions.