  We consider the problem of constructing a reduced-rank regression model whose
coefficient parameter is represented as a singular value decomposition with
sparse singular vectors. The traditional estimation procedure for the
coefficient parameter often fails when the true rank of the parameter is high.
To overcome this issue, we develop an estimation algorithm with rank and
variable selection via sparse regularization and manifold optimization, which
enables us to obtain an accurate estimation of the coefficient parameter even
if the true rank of the coefficient parameter is high. Using sparse
regularization, we can also select an optimal value of the rank. We conduct
Monte Carlo experiments and real data analysis to illustrate the effectiveness
of our proposed method.
