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

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 efficient 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 and efficient supervised data reduction.