Robust discriminant analysis with adaptive locality preserving

Conventional linear discriminant analysis methods commonly ignore the information loss and locality preserving, which greatly limits their performance. To address these issues, we propose a novel discriminant analysis method for feature extraction in this paper. Specially, the proposed method simultaneously exploits the local information and label information to guide the projection learning by constraining the margins of samples from the same class with an adaptively learned weighted matrix, which enables the method to obtain a more compact and discriminative projection. To catch as much discriminant information as possible, a variant of principle component analysis (PCA) term is further introduced to constrain the projection. Besides, to reduce the negative influence of noise and redundant features, a spares error term and a sparse projection constraint are simultaneously introduced to the framework, which enables the method to adaptively select those important features during feature extraction. Compared with the other methods, the proposed method simultaneously holds many good properties including discriminability, locality, data reconstruction, and feature selection in a framework, and is robust to noise. These good properties encourage the method to perform better than the other methods. Extensive experimental results conducted on face, object, scene, and noisy databases verify the effectiveness of the proposed in feature extraction.