An inexact proximal DC algorithm with sieving strategy for rank constrained least squares semidefinite programming

TL;DR

This paper introduces an inexact proximal DC algorithm with a sieving strategy to efficiently solve rank constrained least squares semidefinite programming problems, improving data dimension reduction and face recognition accuracy.

Contribution

It proposes a novel inexact proximal DC algorithm with sieving strategy for rank constrained semidefinite programming, demonstrating improved efficiency and effectiveness over existing methods.

Findings

s-iPDCA outperforms classical PDCA and PDCAe in efficiency

The proposed method achieves competitive recognition accuracy

The algorithm converges globally to stationary points

Abstract

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).