Two-dimensional sparse principal component analysis for face recognition

Principal Component Analysis (PCA) is a wellknown and efficient technique for feature extraction and dimension reduction, which has been applied widely in community of machine learning and pattern recognition. But traditional PCA suffers from two disadvantages which restricts it´s treatment of two dimensional data, like human faces, fingerprints, palmprints and other biological features which are usually represented by two dimensional image matrices. To perform the traditional PCA, the first work is to transform 2-d image matrices to 1-d vectors. But such matrix-to-vector transformation ignores the underlying local data structure and results in difficulty of dealing with high dimensional vectors. Secondly, transformed features are difficult to explain because each principal component is a linear combination of all original features, which is not appropriate for further data analysis. To overcome above two drawbacks, we proposed a novel approach 2dSPCA, namely two-dimensional Sparse Principal Component Analysis. 2dSPCA directly uses 2-d image instead of 1-d vector to compute covariance matrix, which reserves the local structure of face image and reduces significantly the dimension of covariance matrix, so the results are better for data representation and the computation of eigenvalue decomposition is more efficient. Furthermore, we transform eigenvalue decomposition problem to a ridge regression problem by the image covariance matrix, then imposes l₁ constraint on the regression coefficients to obtain sparse loadings. Since the problem is transformed to a Elastic Net optimization problem, the sparse loadings can be easily solved by LARS-EN algorithm. Sparsity makes the results more interpretable and easier to find the intrinsic relation among variables. We also proposed a supervised algorithm 2dSPCA+LDA to improve the recognition rate. Experimental results on face recognition show that both 2dSPCA and 2dSPCA+LDA achieve comparable or higher performance c- - ompared with 1-d cases.