Two-way Spectrum Pursuit for CUR Decomposition and Its Application in Joint Column/Row Subset Selection
This addresses the need for efficient matrix approximation in various domains, but it appears incremental as it builds on existing CUR decomposition methods.
The paper tackles the problem of simultaneous column and row subset selection by proposing an iterative algorithm called two-way spectrum pursuit (TWSP) that captures structural information from actual columns and rows, providing an accurate solution for CUR matrix decomposition with linear complexity. It demonstrates applications in cognitive radio networks, user-content detection, and supervised data reduction.
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.