Abstract

A third-order tensor may be decomposed into three column-wise orthogonal matrices A, B, and C, and a core array G. There are several methods to find these entities, the most classic is the Tucker decomposition that simultaneously determines the arrays by minimizing a mean-squared loss function. The search algorithm consists of an alternating least square algorithm whose iterative process includes Kronecker products and the factorization of unfolding matrices. These tasks are computationally demanding when analyzing large data sets. Efforts have focused on improving the numerical and computational implementations of the algorithms in such a way that they are more efficient in terms of execution times and convergence properties. A multilinear singular value decomposition (HOSVD) has been also proposed to factor tensors. In this work, we present a performance comparison study of factorization algorithms for the analysis of streaming third-order tensors. We investigate the ALS algorithms with their variants eigen-ALS, SVD-ALS, and NIPALS-ALS. In addition, a new procedure called ISVD-ALS is examined. This algorithm considers the incremental singular value decomposition algorithm to factor unfolding matrices. Three metrics are inspected by performing numerical experiments on synthetic data and a real-data application: time savings, number of iterations, and fit ratio.