Essence of Two-Dimensional Principal Component Analysis

The technique of two-dimensional principal component analysis (2DPCA) is analyzed and its essence is revealed. The image total scatter matrix of 2DPCA is in nature equivalent to the sum of all total scatter matrices of m training subsets in which the kth subset is formed by the kth line of each of all training images, where m is the number of lines contained in an image. Based on this result, the true reason why 2DPCA outperforms PCA is uncovered, i.e., different from the traditional PCA using only global information of images, 2DPCA combines the local and global information of images simultaneously and alternative more transparent and understandable 2DPCA algorithm is developed. Finally, some relations to PCA and MPCA and 2DPCA are shown.