Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:A1L-D
Session:
Number:A1L-D3
Multi-way Nonnegative Tensor Factorization Using Fast Hierarchical Alternating Least Squares Algorithm (HALS)
Anh Huy PHAN, Andrzej CICHOCKI,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
In this paper we derive a new fast and efficient iterative algorithm for N-th order Nonnegative Tensor Factorization (NTF). We propose to use a set of local cost functions whose simultaneous or sequential (one by one) minimization via a projected gradient technique leads to simple and very efficient algorithm. The proposed algorithm exploits nonlinear projected gradient and fixed point approaches and it is a natural extension of our Hierarchical-Alternating Least Squares (HALS) algorithm developed for Nonnegative Matrix Factorization (NMF) and NTF2 for sparse and noisy data. In the special case, the proposed algorithm reduces to an improved fast HALS algorithm for the standard NMF. Extensive computer simulations confirmed validity and excellent convergence properties of the proposed algorithm.