Randomized Nonnegative Tensor Factorization for Feature Extraction from High-dimensional Signals

Abstract

Tensor decomposition methods are well-known tools for multilinear feature extraction from multi-way arrays with many important applications in signal processing and machine learning. Nonnegative Tensor Factorization (NTF) is a particular case of such methods, mostly addressed for processing nonnegative multi-way arrays, such as hyperspectral observations or a set of images. One of the most efficient algorithms for NTF is the Hierarchical Alternating Least Squares (HALS) algorithm that belongs to a family of coordinate gradient descent updates. Despite its very good numerical properties, its computational complexity is quite large for large-scale datasets. In this study, we propose the randomized extension of the HALS, which considerably decreases its computational complexity with respect to the standard HALS. The numerical experiments, performed for various large-scale observations, confirm that the proposed algorithm is much faster than the standard one at the cost of slightly decreased performance.