An efficient regularized neighborhood discriminant analysis through QR decomposition

Inspired by the concept of manifold learning, the discriminant embedding technologies aim to exploit low dimensional discriminant manifold structure in the high dimensional space for dimension reduction and classification. However, such graph embedding framework based techniques usually suffer from the large complexity and small sample size (SSS) problem. To address the problem, we reformulate the Laplacian matrix and propose a regularized neighborhood discriminant analysis method, namely RNDA, to discover the local discriminant information, which follows similar approach to regularized LDA. Compared with other discriminant embedding techniques, RNDA achieves efficiency by employing the QR decomposition as a pre-step. Experiments on face databases are presented to show the outstanding performance of the proposed method.