A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition

TL;DR

This paper introduces a rank-adaptive higher-order orthogonal iteration algorithm for efficient and accurate truncated Tucker decomposition of tensors, with proven convergence and demonstrated advantages in experiments.

Contribution

It presents a novel rank-adaptive HOOI algorithm with convergence proof, improving tensor decomposition accuracy and efficiency over existing methods.

Findings

The proposed algorithm converges monotonically and is locally optimal.

Numerical experiments show improved accuracy and efficiency.

Theoretical analysis explains the benefits of rank adaptivity.

Abstract

We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI) algorithm to compute the truncated Tucker decomposition of higher-order tensors with a given error tolerance, and prove that the method is locally optimal and monotonically convergent. A series of numerical experiments related to both synthetic and real-world tensors are carried out to show that the proposed rank-adaptive HOOI algorithm is advantageous in terms of both accuracy and efficiency. Some further analysis on the HOOI algorithm and the classical alternating least squares method are presented to further understand why rank adaptivity can be introduced into the HOOI algorithm and how it works.