Kernel locality-constrained collaborative representation based discriminant analysis

Collaborative representation based classifier (CRC) has been successfully applied to pattern classification. However, CRC may not be able to identify the data with highly nonlinear distribution as a linear algorithm. In this paper, we first propose a kernel locality-constrained collaborative representation based classifier (KLCRC). KLCRC is a nonlinear extension of CRC, and it introduces the local structures of data sets into collaborative representation methods. Since the kernel feature space has a very high (or possibly infinite) dimensionality, we present a dimensionality reduction method (termed kernel locality-constrained collaborative representation based discriminant analysis, KLCR-DA) which can fit KLCRC well. KLCR-DA seeks a subspace in which the between-class reconstruction residual of a given data set is maximized and the within-class reconstruction residual is minimized. Hence, KLCRC can achieve better performances in the projected space. Extensive experimental results on AR, the extended Yale B, FERET face image databases and HK PloyU palmprint database show the superiority of KLCR-DA in comparison to the related methods.