Some Convergence Results on the Regularized Alternating Least-Squares Method for Tensor Decomposition

TL;DR

This paper analyzes the convergence properties of the Regularized Alternating Least-Squares (RALS) algorithm for tensor decomposition, demonstrating that under certain conditions, its limit points are critical points of the cost functional, with numerical evidence of faster convergence.

Contribution

The paper provides new convergence results for RALS in tensor decomposition and compares its performance to standard ALS, showing improved convergence behavior.

Findings

RALS limit points are critical points of the cost functional

Numerical examples show RALS converges faster than ALS

Convergence results depend on the existence of critical points

Abstract

We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergence rate for the RALS in comparison to the usual alternating least squares method.