Feature space locality constraint for kernel based nonlinear discriminant analysis

Subspace learning is an important approach in pattern recognition. Nonlinear discriminant analysis (NDA), due to its capability of describing nonlinear manifold structure of samples, is considered to be more powerful to undertake classification tasks in image related problems. In kernel based NDA representation, there are three spaces involved, i.e., original data space, implicitly mapped high dimension feature space and the target low dimension subspace. Existing methods mainly focus on the information in original data space to find the most discriminant low dimension subspace. The implicit high dimension feature space plays a role that connects the original space and the target subspace to realize the nonlinear dimension reduction, but the sample geometric structure information in feature space is not involved. In this work, we try to utilize and explore this information. Specifically, the locality information of samples in feature space is modeled and integrated into the traditional kernel based NDA methods. In this way, both the sample distributions in original data space and the mapped high dimension feature space are modeled and more information is expected to be explored to improve the discriminative ability of the subspace. Two algorithms, named FSLC-KDA and FSLC-KSR, are presented. Extensive experiments on ORL, Extended-YaleB, PIE, Multi-PIE and FRGC databases validate the efficacy of the proposed method.

► The relationship of three spaces in nonlinear discriminant analysis is analyzed.
► Locality constraint in mapped high dimension feature space is proposed and integrated into the nonlinear discriminant analysis method.
► Two examples FSLC-KDA and FSLC-KSR are presented to show how FSLC can be integrated with the existing NDA methods.
► The linear version of FSLC based method is presented.
► Extensive experiments are conducted to show the superiority of the proposed FSLC based methods.