  In this paper, the optimization problem of the supervised distance preserving
projection (SDPP) for data dimension reduction (DR) is considered, which is
equivalent to a rank constrained least squares semidefinite programming
(RCLSSDP). In order to overcome the difficulties caused by rank constraint, the
difference-of-convex (DC) regularization strategy was employed, then the
RCLSSDP is transferred into a series of least squares semidefinite programming
with DC regularization (DCLSSDP). An inexact proximal DC algorithm with sieving
strategy (s-iPDCA) is proposed for solving the DCLSSDP, whose subproblems are
solved by the accelerated block coordinate descent (ABCD) method. Convergence
analysis shows that the generated sequence of s-iPDCA globally converges to
stationary points of the corresponding DC problem. To show the efficiency of
our proposed algorithm for solving the RCLSSDP, the s-iPDCA is compared with
classical proximal DC algorithm (PDCA) and the PDCA with extrapolation (PDCAe)
by performing DR experiment on the COIL-20 database, the results show that the
s-iPDCA outperforms the PDCA and the PDCAe in solving efficiency. Moreover, DR
experiments for face recognition on the ORL database and the YaleB database
demonstrate that the rank constrained kernel SDPP (RCKSDPP) is effective and
competitive by comparing the recognition accuracy with kernel semidefinite SDPP
(KSSDPP) and kernal principal component analysis (KPCA).
