Novel Multi-layer Non-negative Tensor Factorization with Sparsity Constraints

Authors:
Andrzej Cichocki;Rafal Zdunek;Seungjin Choi;Robert Plemmons;Shun-Ichi Amari
Affiliations:
RIKEN Brain Science Institute, Wako-shi, Japan;RIKEN Brain Science Institute, Wako-shi, Japan;POSTECH, Korea;Dept. of Mathematics and Computer Science, Wake Forest University, USA;RIKEN Brain Science Institute, Wako-shi, Japan
Venue:
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part II
Year:
2007

Citing 7
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Abstract

In this paper we present a new method of 3D non-negative tensor factorization (NTF) that is robust in the presence of noise and has many potential applications, including multi-way blind source separation (BSS), multi-sensory or multi-dimensional data analysis, and sparse image coding. We consider alpha- and beta-divergences as error (cost) functions and derive three different algorithms: (1) multiplicative updating; (2) fixed point alternating least squares (FPALS); (3) alternating interior-point gradient (AIPG) algorithm. We also incorporate these algorithms into multilayer networks. Experimental results confirm the very useful behavior of our multilayer 3D NTF algorithms with multi-start initializations.