On Accelerating the Regularized Alternating Least Square Algorithm for Tensors

TL;DR

This paper introduces an accelerated version of the regularized alternating least squares algorithm for tensor approximation, achieving faster convergence through Aitken-Stefensen-like updates and providing theoretical convergence analysis.

Contribution

The paper proposes a novel accelerated RALS algorithm with Aitken-Stefensen updates and analyzes its convergence properties, improving tensor approximation efficiency.

Findings

Accelerated RALS converges faster than standard RALS.

Numerical experiments confirm improved convergence rates.

Theoretical analysis shows linear local convergence.

Abstract

In this paper, we discuss the acceleration of the regularized alternating least square (RALS) algorithm for tensor approximation. We propose a fast iterative method using a Aitken-Stefensen like updates for the regularized algorithm. Through numerical experiments, the fast algorithm demonstrate a faster convergence rate for the accelerated version in comparison to both the standard and regularized alternating least squares algorithms. In addition, we analyze the global convergence based on the Kurdyka- Lojasiewicz inequality as well as show that the RALS algorithm has a linear local convergence rate.