ORTHOGONAL LOW-RANK APPROXIMATION TO THIRD-ORDER TENSORS WITH AUTOMATIC RANK ESTIMATION

摘要

The purpose of this work is to automatically estimate the rank parameter in the problem of orthogonal low-rank approximation to higher-order tensors. To this end, we view the coefficients of the latent rank-1 terms in the model as a vector to be sparsified, where an exponentially induced regularizer is employed to gain the sparsity. The sparsity of the coefficient vector controls the low-rankness of the model. By exploring the reweighted property of the regularizer, we propose a reweighted type alternating least squares algorithm to solve the model, and its convergence is established without any assumption. Preliminarily numerical experiments show that the proposed model and algorithm can provide a valid estimate of the number of rank-1 terms.