Orthogonal neighborhood preserving discriminant analysis with patch embedding for face recognition

Abstract

Intuitively, all facial images of a person are located on or near a manifold in the high-dimensional image space, and the process of face recognition can be regarded as the recovery process of multiple low-dimensional manifolds. To preserve the manifold structure information of intra-class samples after dimensionality reduction, we proposed a patch-based multi-manifold orthogonal neighborhood-preserving discriminant analysis algorithm, namely ONPDA. From the perspective of path alignment, we consider the intra-class compactness, intra-class structure and inter-class separability simultaneously. Moreover, we infuse intra-class structure information described by the sample reconstruction into intra-class compactness loss, considering the compactness of two reconstruction groups instead of sample pairs in the same class. By analyzing the relationship between the projection direction and the maximum inter-class margin, we select the samples that should participate in the inter-class separability on the patch. Meanwhile, a fast orthogonalization method is performed to obtain the orthogonal projection matrix. Besides, we perform ONPDA in reproducing kernel Hilbert space which gives rise to nonlinear maps, resulting in the kernel ONPDA (KONPDA). Experimental results compared with some state-of-the-art methods on a toy dataset and several benchmark face image databases demonstrate the effectiveness of ONPDA and KONPDA.