Linear Laplacian Discrimination for Feature Extraction - PKU.pdfVIP

Linear Laplacian Discrimination for Feature Extraction Deli Zhao Zhouchen Lin Rong Xiao Xiaoou Tang Microsoft Research Asia, Beijing, China delizhao@, {zhoulin,rxiao,xitang}@ Abstract underlying structures and characteristics of different classes. Discriminant features are often obtained by class- Discriminant feature extraction plays a fundamental role supervised learning. Linear discriminant analysis (LDA) is in pattern recognition. In this paper, we propose the Lin- the traditional approach to learning discriminant subspaces ear Laplacian Discrimination (LLD) algorithm for discrim- where the between-class scatter of samples is maximized inant feature extraction. LLD is an extension of Linear and the within-class scatter is minimized at the same time. Discriminant Analysis (LDA). Our motivation is to address The Fisherfaces algorithm [3] and many variants of LDA the issue that LDA cannot work well in cases where sam- hae shown good performance in face recognition in com- ple spaces are non-Euclidean. Specifically, we define the plex scenarios. [24, 9, 20, 22, 11, 12, 28]. By defining within-class scatter and the between-class scatter using the representations of intra-personal and extra-personal dif- similarities which are based on pairwise distances in sam- ferences, Bayesian face recognition [2] proposes another ple spaces. Thus the structural information of classes is way to explore discriminant features via probabilistic simi- contained in the within-class and the between-class Lapla- larity measure. The inherent connection between LDA and cian