caa a22 4500 445871423 CHVBK 20180317145513.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s10618-010-0196-4 doi (NATIONALLICENCE)springer-10.1007/s10618-010-0196-4 Nonnegative tensor factorization as an alternative Csiszar-Tusnady procedure: algorithms, convergence, probabilistic interpretations and novel probabilistic tensor latent variable analysis algorithms [Elektronische Daten] [Stefanos Zafeiriou, Maria Petrou] 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. The Author(s), 2010 Nonnegative Matrix Factorization nationallicence Nonnegative Tensor Factorization nationallicence Kullback-Leibler divergence nationallicence Probabilistic Latent Semantic Analysis nationallicence Zafeiriou Stefanos Department of Electrical and Electronic Engineering, Imperial College London, Signal Processing and Communication Research Group, South Kensington Campus, SW7 2AZ, London, UK aut Petrou Maria Department of Electrical and Electronic Engineering, Imperial College London, Signal Processing and Communication Research Group, South Kensington Campus, SW7 2AZ, London, UK aut Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 22/3(2011-05-01), 419-466 1384-5810 22:3<419 2011 22 10618 https://doi.org/10.1007/s10618-010-0196-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10618-010-0196-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zafeiriou Stefanos Department of Electrical and Electronic Engineering, Imperial College London, Signal Processing and Communication Research Group, South Kensington Campus, SW7 2AZ, London, UK aut NATIONALLICENCE 700 1- Petrou Maria Department of Electrical and Electronic Engineering, Imperial College London, Signal Processing and Communication Research Group, South Kensington Campus, SW7 2AZ, London, UK aut NATIONALLICENCE 773 0- Data Mining and Knowledge Discovery Springer US; http://www.springer-ny.com 22/3(2011-05-01), 419-466 1384-5810 22:3<419 2011 22 10618 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer