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

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. 1 Models and Problem Formulation Tensors (also known as n-way arrays or multidimensional arrays) are used in a variety of applications ranging from neuroscience and psychometrics to chemometrics [1–4]. Nonnegative matrix factorization (NMF), Non-negative tensor factorization (N...

• Type: Conference
• Year: 2007
• Where: ICANNGA
• Authors: Andrzej Cichocki, Rafal Zdunek, Seungjin Choi, Robert J. Plemmons, Shun-ichi Amari
• Keywords: ICANNGA 2007, Non-negative Tensor Factorization, NTF Algorithms, flexible Ntf Algorithms