A novel margin-based linear embedding technique for visual object recognition

Abstract

Linear Dimensionality Reduction (LDR) techniques have been increasingly important in computer vision and pattern recognition since they permit a relatively simple mapping of data onto a lower dimensional subspace, leading to simple and computationally efficient classification strategies. Recently, many linear discriminant methods have been developed in order to reduce the dimensionality of visual data and to enhance the discrimination between different groups or classes. Although many linear discriminant analysis methods have been proposed in the literature, they suffer from at least one of the following shortcomings: i) they require the setting of many parameters (e.g., the neighborhood sizes for homogeneous and heterogeneous samples), ii) they suffer from the Small Sample Size problem that often occurs when dealing with visual data sets for which the number of samples is less than the dimension of the sample, and iii) most of the traditional subspace learning methods have to determine the dimension of the projected space by either cross-validation or exhaustive search. In this paper, we propose a novel margin-based linear embedding method that exploits the nearest hit and the nearest miss samples only. Our proposed method tackles all the above shortcomings. It finds the projection directions such that the sum of local margins is maximized. Our proposed approach has been applied to the problem of appearancebased face recognition. Experimental results performed on four public face databases show that the proposed approach can give better generalization performance than the competing methods. These competing methods used for performance comparison were: Principal Component Analysis (PCA), Locality Preserving Projections (LPP), Average Neighborhood Margin Maximization (ANMM), and Maximally Collapsing Metric Learning algorithm (MCML). The proposed approach could also be applied to other category of objects characterized by large variations in their appearance.