Directional Principal Component Analysis for Image Matrix

In this paper, we present a novel approach, namely directional multi-mode principal component analysis, which efficiently avoids the small sample size problem and preserves the spatial information embed in among pixels of image, by encoding the input high-dimensional image as a tensor. In the proposed scheme, the mode-k matrix of the image is re-sampled and re-arranged to form a mode-k directional image for better exploiting the local structure information in training. An algorithm called mode-k direction Principal Component Analysis (PCA) is then presented to learn the multiple interrelated lower-dimensional subspaces without iterative step. Compared with conventional and other subspace analysis algorithms, the proposed method can greatly alleviate the small sample size problem, avoid the curse of dimensionality, reduce the computational cost in the learning stage by representing the data in lower dimension, and simultaneously exploit the local structural information embedded in the high dimensional dataset. Experimental results on well-known AR and UMIST databases show that the proposed method has higher recognition accuracy than many traditional subspace learning algorithms while using a low dimension of features.