Simultaneous p- and s-orders minmax robust locality preserving projection

Abstract

This paper proposes a new method of locality preserving projection (LPP), which replaces the squared L2-norm minimization and maximization distances in the objective of conventional LPPW. The proposed method is termed as Simultaneous p- and s-orders Minmax Robust Locality Preserving Projection (psRLPP), which is robust to outlier samples. Then, we design an efficient iterative algorithm to solve the objective problem of psRLPP. At each iteration, our method ends with solving a trace ratio problem rather inexact ratio trace problem. We also conduct some insightful analysis on the existence of local minimum and the convergence of the proposed algorithm. These characteristics make our psRLPP more intuitive and powerful than the most up-to-date method, robust LPP via p-order minimization (RLPP) which considers only the p-order minimization of the L2-norm distance and requires transforming the original trace ratio problem in each iteration into an inexact ratio problem in the solving of projection vectors. Theoretical insights and effectiveness of our method is further supported by promising experimental results for clustering.