Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis

Abstract

Recently, L1-norm distance measure based Linear Discriminant Analysis (LDA) techniques have been shown to be robust against outliers. However, these methods have no guarantee of obtaining a satisfactory-enough performance due to the insufficient robustness of L1-norm measure. To mitigate this problem, inspired by recent works on Lp-norm based learning, this paper proposes a new discriminant method, called Lp- and Ls-Norm Distance Based Robust Linear Discriminant Analysis (FLDA-Lsp). The proposed method achieves robustness by replacing the L2-norm within- and between-class distances in conventional LDA with Lp- and Ls-norm ones. By specifying the values of p and s, many of previous efforts can be naturally expressed by our objective. The requirement of simultaneously maximizing and minimizing a number of Lp- and Ls-norm terms results in a difficulty to the optimization of the formulated objective. As one of the important contributions of this paper, we design an efficient iterative algorithm to address this problem, and also conduct some insightful analysis on the existence of local minimum and the convergence of the proposed algorithm. Theoretical insights of our method are further supported by promising experimental results on several images databases.

Keywords: Lp-norm; Ls-norm; Robustness; linear Discriminant Analysis.