A regularized least square based discriminative projections for feature extraction

In this paper, we present a regularized least square based discriminative projections (RLSDP) method for feature extraction. First, we show that both sparse representation based classifier (SRC) and collaborative representation based classification (CRC) are regularized least square in nature. Second, a regularized least square based graph embedding framework (RLSGE) is constructed. Third, a RLSGE based feature extraction method is given, named regularized least square based discriminant projections (RLSDP). In RLSDP, the within-class compactness information is characterized by the reconstruction residual from the same class, which is consistent with the idea of reconstruction; the between-class separability information is characterized by the between-class scatter matrix like Fisher LDA. RLSDP is much faster than SPP since RLSDP adopts the L2 norm constraint while SPP adopts the L1 norm constraint. The experimental results on AR face database, FERET face database, and the PolyU FKP database demonstrate that RLSDP works well in feature extraction and has a great recognition performance.