Local and Weighted Maximum Margin Discriminant Analysis

Abstract

In this paper, we propose a new approach, called local and weighted maximum margin discriminant analysis (LWMMDA), to performing object discrimination. LWMMDA is a subspace learning method that identifies the underlying nonlinear manifold for discrimination. The goal of LWMMDA is to seek a transformation such that data points of different classes are projected as far as possible while points within a same class are as compact as possible. The projections are obtained by maximizing a new discriminant criterion, called local and weighted maximum margin criterion (LWMMC). Different from previous maximum margin criterion (MMC) which seeks only the globally Euclidean structure of data points, LWMMC takes the local property into account, which makes LWMMC more accurate in finding discriminant information. LWMMC has an additional weighted parameter β that further broadens the average margin between different classes. Computationally, LWMMDA completely avoids the singularity problem. Besides, LWMMDA couples the QR-decomposition into its framework, which makes LWMMDA very efficient and stable in implementation. Finally, LWMMDA framework is straightforwardly extended into the reproducing kernel Hilbert space induced by a nonlinear function ϕ. Experiments on digit visualization, face recognition, and facial expression recognition are presented to show the effectiveness of the proposed method.