Stochastic Iterative Hard Thresholding for Low-Tucker-Rank Tensor Recovery

TL;DR

This paper introduces a stochastic iterative hard thresholding algorithm tailored for low-Tucker-rank tensor recovery, providing convergence analysis and demonstrating effectiveness through experiments on synthetic and real data.

Contribution

It extends stochastic iterative hard thresholding to the tensor domain for low-Tucker-rank recovery, with proven linear convergence and empirical validation.

Findings

The proposed algorithm achieves linear convergence.

It performs well on synthetic and real datasets.

The method effectively recovers low-Tucker-rank tensors from linear measurements.

Abstract

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years, researchers have developed many state-of-the-art algorithms to address the problem of low-Tucker-rank tensor recovery. Motivated by the favorable properties of the stochastic algorithms, such as stochastic gradient descent and stochastic iterative hard thresholding, we aim to extend the well-known stochastic iterative hard thresholding algorithm to the tensor framework in order to address the problem of recovering a low-Tucker-rank tensor from its linear measurements. We have also developed linear convergence analysis for the proposed method and conducted a series of experiments with both synthetic and real data to illustrate the performance of the proposed method.