While null space based linear discriminant analysis (NLDA) obtains a good discriminant performance, the ability easily suffers from an implicit assumption of Gaussian model with same covariance each class. Meanwhile, mixture model discriminant analysis, which is a good way for processing issues on multiple subclasses in each class, depends on human experience on the number of subclasses and has a highly complex iterative process. Considering the cons and pros of the two mentioned approaches, we

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... therefore propose a new algorithm, called Spectral clustering based Null space Linear Discriminant Analysis (SNLDA). The main contributions of the algorithm include the following three aspects: 1) Employing a new spectral clustering method which can automatically detect the number of clusters in each class. 2) Finding a unified null space for processing multi-subclasses issues with eigen-solution technique. 3) Refining the calculation of the covariance matrix in a single sample subclass. The experimental results show the promising of the proposed SNLDA algorithm.