  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.
