Two-way Spectrum Pursuit for CUR Decomposition and Its Application in Joint Column/Row Subset Selection

TL;DR

This paper introduces Two-way Spectrum Pursuit (TWSP), an iterative algorithm for selecting actual columns and rows to improve CUR matrix decomposition, with broad applications in signal processing and data reduction.

Contribution

The paper proposes TWSP, a novel iterative method for joint column and row subset selection that accurately captures matrix structure with linear complexity.

Findings

TWSP effectively captures structural information of matrices.

TWSP achieves accurate CUR decomposition in various applications.

The algorithm has linear complexity relative to the number of columns and rows.

Abstract

The problem of simultaneous column and row subset selection is addressed in this paper. The column space and row space of a matrix are spanned by its left and right singular vectors, respectively. However, the singular vectors are not within actual columns/rows of the matrix. In this paper, an iterative approach is proposed to capture the most structural information of columns/rows via selecting a subset of actual columns/rows. This algorithm is referred to as two-way spectrum pursuit (TWSP) which provides us with an accurate solution for the CUR matrix decomposition. TWSP is applicable in a wide range of applications since it enjoys a linear complexity w.r.t. number of original columns/rows. We demonstrated the application of TWSP for joint channel and sensor selection in cognitive radio networks, informative users and contents detection, and efficient supervised data reduction.