Weighted Discriminant Tensor Criterion Based Face Recognition

Feature extraction has been the technical difficulty and research priority and in face recognition. For the advantage of the multi-dimensional property, tensor data can effectively express the human face image and ensure the integrity of its structure. Multi-linear algebra provides effective data analysis methods for tensor data, therefore multi-linear extension of linear discriminant analysis is becoming a research hotspot.Firstly, in the multi-class recognition problem, the existing Fisher criterion based discriminant analysis methods overemphasize the leading role of marginal category in the feature decomposition process. To solve this problem, we propose the pair-wise weighted discriminant tensor criterion(WDTC). Based on the principle of setting a higher weight value on the classes of smaller inter-class distance, WDTC utilizes the simple and efficient Euclidean distance to design weight function and revises the inter-class scatter of tensor sample sets. On this basis, we propose weighted tensor discriminant analysis(WTDA) to improve the discriminant performance of the tensor discriminant analysis methods.Secondly, the features extracted by WTDA are generally statistically correlated and there still exists some redundant information. Therefore, we propose weighted discriminant tensor criterion based uncorrelated discriminant analysis(WDTUDA). It adds uncorrelated constraints to WDTC and iterative solves the uncorrelated feature in the tensor subspace.Finally, consider that most data sets are not Gaussian distribution, there may exist some deviation for that WDTUDA uses the mean of all tensor samples to estimate the expectation. Based on this, this paper utilizes the local information of samples to construct local total scatter matrix and proposes weighted discriminant tensor criterion based local uncorrelated discriminant analysis(WDTLUDA). The feature extracted by WDTLUDA not only gains the global discriminant ability,but also eliminates redundant information between local samples. Furthermore, we extract the principal component feature and linear discriminant feature to enrich the original tensor sample and further enhance the recognition performance.