Learning in multimodal and mixmodal data: locality preserving discriminant analysis with kernel and sparse representation techniques

Abstract

We consider the problem of feature extraction for “multimodal” and “mixmodal” data. A new supervised learning method called locality preserving discriminant analysis (LPDA) is presented, which aims to maximize the weighted between-class distances and minimize the locality-preserved within-class distances. By introducing a specific affinity matrix for each class, LPDA can better preserve the local geometric structure of the samples within it, and thus efficiently derive nonlinear characters of the data structure. Meanwhile, by using the defined between-class weight matrix, LPDA also preserves the interrelation information of data from different classes. This facilitates the separation of between-class data. We further extend LPDA to kernel-LPDA and sparse-LPDA by taking advantage of theories of kernel technique and sparse representation. Experiments for data classification, handwriting and face recognition are carried out to verify the feasibility and effectiveness of the proposed approaches.