Projection-based QLP Algorithm for Efficiently Computing Low-Rank Approximation of Matrices

TL;DR

This paper introduces the Projection-based Partial QLP (PbP-QLP), a new randomized algorithm that efficiently approximates the pivoted QLP for low-rank matrices, leveraging modern architectures for improved performance.

Contribution

The paper presents a novel randomized PbP-QLP algorithm that avoids pivoting, offering high-accuracy low-rank approximation with better computational efficiency.

Findings

PbP-QLP achieves high accuracy comparable to p-QLP.

The algorithm outperforms existing randomized methods in efficiency.

Effective on both synthetic and real-world data matrices.

Abstract

Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is computationally prohibitive for large matrices. In this paper, we introduce a new algorithm termed Projection-based Partial QLP (PbP-QLP) that efficiently approximates the p-QLP with high accuracy. Fundamental in our work is the exploitation of randomization and in contrast to the p-QLP, PbP-QLP does not use the pivoting strategy. As such, PbP-QLP can harness modern computer architectures, even better than competing randomized algorithms. The efficiency and effectiveness of our proposed PbP-QLP algorithm are investigated through various classes of synthetic and real-world data matrices.