Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization

In the paper we present new Alternating Least Squares (ALS) algorithms for Nonnegative Matrix Factorization (NMF) and their extensions to 3D Nonnegative Tensor Factorization (NTF) that are robust in the presence of noise and have many potential applications, including multi-way Blind Source Separation (BSS), multi-sensory or multidimensional data analysis, and nonnegative neural sparse coding. We propose to use local cost functions whose simultaneous or hierarchical (one by one) minimization leads to a very simple ALS algorithm which works under some sparsity constraints both for an under-determined (a system which has less sensors than sources) and over-determined model. The extensive experimental results confirm the validity and high performance of the developed algorithms, especially with usage of the multilayer NMF.

• Type: Conference
• Year: 2007
• Where: ICA
• Authors: Andrzej Cichocki, Rafal Zdunek, Shun-ichi Amari
• Keywords: ICA 2007, Nonnegative Matrix Factorization, Nonnegative Neural Sparse, Nonnegative Tensor Factorization, Signal Processing