Discriminant Hyper-Laplacian projections with its application to face recognition

Discriminant Locality Preserving Projections (DLPP) is one of the most influential supervised subspace learning algorithms that considers both discriminative and geometric (manifold) information. There is an obvious drawback of DLPP that it only considers the pairwise geometric relationship of samples. However, in many real-world issues, relationships among the samples are often more complex than pairwise. Naively squeezing the complex into pairwise ones will inevitably lead to loss of some information, which are crucial for classification and clustering. We address this issue via using the Hyper-Laplacian instead of the regular Laplacian in DLPP, which only can depict the pairwise relationship. This new DLPP algorithm is exactly a generalization of DLPP and we name it Discriminant Hyper-Laplacian Projection (DHLP). Five popular face databases are adopted for validating our work. The results demonstrate the superiority of DHLP over DLPP, particularly in face recognition in the wild.