Sample and Expand: Discovering Low-rank Submatrices With Quality Guarantees

TL;DR

This paper introduces a two-phase method for discovering low-rank submatrices within larger matrices, addressing the challenge that real-world data often contains only localized low-rank structures rather than entire matrices.

Contribution

The paper presents a novel sampling and expansion approach for identifying low-rank submatrices with quality guarantees, improving over existing methods.

Findings

Method effectively discovers low-rank submatrices in real-world data.

Experimental results show favorable comparison to existing approaches.

Approach preserves proximity to low-rank approximations during expansion.

Abstract

The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the problem of discovering submatrices from the given matrix with bounded deviations from their low-rank approximations. We introduce an effective two-phase method for this task: first, we use sampling to discover small nearly low-rank submatrices, and then they are expanded while preserving proximity to a low-rank approximation. An extensive experimental evaluation confirms that the method we introduce compares favorably to existing approaches.