Locally Supervised Discriminant Analysis in Kernel Space

Considering inherent limitations of such locality-based dimensionality reduction methods as unsupervised discriminant projection (UDP), a novel manifold-base feature extraction method, called locally supervised discriminant analysis in kernel space, is proposed in the paper. It is a locally nonlinear and supervised dimensionality reduction method, which takes into account the locality, kernel mapping and class information simultaneously in the process of feature extraction. The proposed algorithm seeks to find a projection that maximizes the kernel non-local scatter, while minimizes the kernel local scatter and the kernel within-class scatter. As a result, the final projection vectors could have more powerful discriminant abilities since it not only captures the intrinsic nonlinear change of data, but also preserve the faithful locality. The experimental results on Yale face database show that the proposed method outperforms the LDA and UDP.