| Feature extraction,known as one of the core issues in pattern recognition,has great significance in both of theoretical research and practical application in terms of computer vision,image processing and machine learning.Extracting effective image features is very helpful to obtain good performance for image recognition.Up to now,many methods in multivariate statistical analysis have been extended and widely used to deal with different problems.The most representative methods are principal component analysis(PCA)and linear discriminant analysis(LDA).PCA has the following advantages: each principal component is not related to each other.Besides,the dimension of the principal component is lower than that of the original data.Also,it can maintain the most important information of the data.However,PCA still has some drawbacks.For example,it does not consider the label information of the data,and thus it is impossible to give clear interpretation for the features.LDA can use label information in the subspace learning process so as to obtain more discriminative features for effective pattern recognition.The limitation of LDA is that it has the small sample size problem,that is,the within-class scatter matrix needs to be non-singular,so that the optimal solution can be obtained by solving the eigen-decomposition problem.Although many LDA-based methods were proposed to release this limitation,they are either sensitive to noise or lack jointly sparse feature selection function.In order to solve the problems mentioned above and improve the performance of PCA and LDA,this paper proposes two methods:(1)A sparse discriminative principal component analysis(SDPCA)algorithm based on PCA is proposed,which introduces traditional least-squares regression into the original objective function of SPCA and use prior knowledge to obtain the principal component with sparsity and discriminative information to improve the performance of feature extraction.(2)A local jointly sparse linear discriminant analysis(LJSLDA)algorithm based on the maximum margin criterion is proposed to integrate the local neighborhood information to construct new within-class scatter matrix and between-class scatter matrix so as to improve performance of discriminant analysis.LJSLDA can not only effectively avoid the small sample size problem in LDA,but also obtain the projections with joint sparsity for efficient feature extraction.The proposed SDPCA and LJSLDA can effectively solve the problems in SPCA and LDA,respectively.This paper also presents some related theoretical analysis,including the differences and connections between SDPCA and SPCA,LJSLDA and LDA.The experiments on face database,handwritten digital database and hyperspectral image database have shown the effectiveness of SDPCA and LJSLDA. |
