Grouping strategy exactly specifies the form of covariance matrix, therefore it is very essential. Most 2DPCA methods use the original 2D image matrices to form the covariance matrix which actually means that the strategy is to group the random variables by row or column of the input image. Because of their grouping strategies these methods have two main drawbacks. Firstly, 2DPCA and some of its variants such as A2DPCA, DiaPCA and MatPCA preserve only the covariance information between the elements of these groups. This directly implies that 2DPCA and these variants eliminate some covariance information while PCA preserves such information that can be useful for recognition. Secondly, all the existing methods suffer from the relatively high intra-group correlation, since the random variables in a row, column, or a block are closely located and highly correlated. To overcome such drawbacks we propose a novel grouping strategy named cross grouping strategy. The algorithm focuses on reducing the redundancy among the row and the column vectors of the image matrix. While doing this the algorithm completely preserves the covariance information of PCA between local geometric structures in the image matrix which is partially maintained in 2DPCA and its variants. And also in the proposed study intra-group correlation is weak according to the 2DPCA and its variants because the random variables spread over the whole face image. These make the proposed algorithm superior to 2DPCA and its variants. In order to achieve this, image cross-covariance matrix is calculated from the summation of the outer products of the column and the row vectors of all images. The singular value decomposition (SVD) is then applied to the image cross-covariance matrix. The right and the left singular vectors of SVD of the image cross-covariance matrix are used as the optimal projective vectors. Further in order to reduce the dimension LDA is applied on the feature space of the proposed method that is proposed method+LDA. The exhaustive experimental results demonstrate that proposed grouping strategy for 2DPCA is superior to 2DPCA, its specified variants and PCA, and proposed method outperforms bi-directional PCA+LDA. 
Cross grouping strategy based 2DPCA method for face recognition