Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization

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