PARAFAC algorithms for large-scale problems

Parallel factor analysis (PARAFAC, called also CP model)) is a tensor (multiway array) factorization method which allows to find hidden factors (component matrices) from a multidimensional data. Most of the existing algorithms for the PARAFAC, especially the alternating least squares (ALS) algorithm need to compute Khatri-Rao products of tall factors and multiplication of large-scale matrices and due to this require high computational cost and large memory and are not suitable for very large-scale problems. Hence, PARAFAC for large-scale data tensors is still a challenging problem. In this paper, we propose a new approach based on a modified ALS algorithm which computes Hadamard products, instead Khatri-Rao products and employs relatively small matrices. The new algorithms are able to process extremely large-scale tensors with billions of entries. Extensive experiments confirm the validity and high performance of the developed algorithms in comparison with other well-known algorithms.