Work

A Preconditioned Riemannian Gradient Descent Algorithm for Low-Rank Matrix Recovery

Year: 2024

Type: article

Abstract: . The low-rank matrix recovery problem often arises in various fields, including signal processing, machine learning, and imaging science. The Riemannian gradient descent (RGD) algorithm has proven to be an efficient algorithm for solving this problem. In this paper, we present a preconditioned Riemannian gradient descent (PRGD) for low-rank matrix recovery. The preconditioner, noted for its simplicity and computational efficiency, is constructed by weighting the [Formula: see text]th entry of the gradient matrix according to the norms of the [Formula: see text]th row and the [Formula: see text]th column. We establish the theoretical recovery guarantee for PRGD under the restricted isometry property assumption. Experimental results indicate that PRGD can accelerate RGD by up to tenfold in solving low-rank matrix recovery problems such as matrix completion.

Source: SIAM Journal on Matrix Analysis and Applications

DOI: 10.1137/23m1570442

Authors: Fengmiao Bian, Jian-Feng Cai, Rui Zhang

Institutions: Hong Kong University of Science and Technology, Huawei Technologies (China)

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Research Grants Council, University Grants Committee, Shanghai Jiao Tong University, Innovation and Technology Fund

Awards: G1114891300, Key Technologies of Artificial Intelligence Applied in Selective Laser Melting Additive Manufacturing, G5710673922, G7209821612