Jointly Sparse Locality Regression for Image Feature Extraction

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This paper proposes a novel method called Jointly Sparse Locality Regression (JSLR) for feature extraction and selection. JSLR utilizes joint $L_{2,1}$ -norm minimization on regularization term, and also introduces the locality to characterize the local geometric structure of the data. There are three main contributions in JSLR for face recognition. Firstly, it eliminates the drawback in ridge regression and Linear Discriminant Analysis (LDA) that when the number of the classes is too small, not enough projections can be obtained for feature extraction. Secondly, by using the local geometric structure as the regularization term, JSLR is able to preserve local information and find an embedding subspace which can detect the most essential data manifold structure. Moreover, since the $L_{2,1}$ -norm based loss function is robust to outliers in data points, JSLR provides the joint sparsity for robust feature selection. The theoretical connections of the proposed method and the previous regression methods are explored and the convergence of the proposed algorithm is also proved. Experimental evaluation on several well-known data sets shows the merits of the proposed method on feature selection and classification.