Local And Global Weighted Uncorrelated Discriminant Transform For Face Recognition

Feature extraction is one of the most important issues in image recognition tasks. In manyapplications such as face recognition, it is meaningful to eliminate the redundancy among theextracted discriminant features. In this paper, we reconstruct the total scatter matrix in order toremove the redundancy among the extracted discriminant features more thoroughly. In this way, wepropose a reformative uncorrelated constraint based on the Fisher linear discriminant algorithms forface recognition. We iteratively calculate the optimal discriminant vectors that maximize the Fishercriterion under the corresponding statistical uncorrelated constraints, respectively.At first, we propose a local uncorrelated discriminant transform (LUDT). LUDT reconstructsthe total scatter matrix by redefining the expectation for each sample using the sample’s neighbourcenter instead of global center, and construct the reformative uncorrelated constraints. Then we putforward another novel uncorrelated discriminant approach, which is weighted global uncorrelateddiscriminant transform (WGUDT). WGUDT reconstructs the total scatter matrix by redefining theexpectation for each sample using Euclidean distance between samples as weighted value toconstruct the expectation, and constructs the reformative uncorrelated constraints. Our approacheseffectively eliminate the redundancy among the extracted discriminate features.In addition, we propose a local kernel uncorrelated discriminant transform (LKUDT) and aweighted global kernel uncorrelated discriminant transform (WGKUDT) based on the reformativetotal scatte, they iteratively calculate the optimal discriminant based on kernel uncorrelatedconstraints, which can eliminate the redundancy among the extracted discriminate features.Moreover, we propose a local two-dimensional uncorrelated discriminant transform (L2DUDT) anda weighted global two-dimensional uncorrelated discriminant transform (WG2DUDT) on the basisof two-dimensional discriminant method. They iteratively calculate the optimal discriminant vectorsbased on two-dimensional uncorrelated constraint, which can not only avoid the singular problem,but also improve the speed of recognition by calculating the scatter matrix without changing imagematrix into column vector.We also propose multi-tasks learning approaches for classification based on LUDT andWGUDT. When the number of training samples is small, we can calculate the LUDT and WGUDTat first and thus improve the dicimination of projection transformation by using other taskes.The proposed approaches are evaluated on the public AR、FERET and CAS-PEAL facedatabases. Experimental results demonstrate that the proposed approaches outperform severalrepresentative feature extraction methods.