Directional independent component analysis with tensor representation

Conventional independent component analysis (ICA) learns the statistical independencies of 2D variables from the training images that are unfolded to vectors. The unfolded vectors, however, make the ICA suffer from the small sample size (SSS) problem that leads to the dimensionality dilemma. This paper presents a novel directional multilinear ICA method to solve those problems by encoding the input image or high dimensional data array as a general tensor. In addition, the mode-k matrix of the tensor is re-sampled and re-arranged to form a mode-k directional image to better exploit the directional information in training. An algorithm called mode-k directional ICA is then presented for feature extraction. Compared with the conventional ICA and other subspace analysis algorithms, the proposed method can greatly alleviate the SSS problem, reduce the computational cost in the learning stage by representing the data in lower dimension, and simultaneously exploit the directional information in the high dimensional dataset. Experimental results on well-known face and palmprint databases show that the proposed method has higher recognition accuracy than many existing ICA, PCA and even supervised FLD schemes while using a low dimension of features.