Tensor canonical correlation analysis

Abstract

In order to decrease the computational time and avoid the singularity of covariance matrix when canonical correlation analysis is used for feature fusion of images, a fast algorithm was proposed. The algorithm considers an image as the second order tensor in RM⊗RN. It is based on two-dimensional image matrices rather than vectors. So, variance and covariance can be constructed using the image matrices by building corresponding criterion function. After getting the projection matrices, it can project the image matrices onto a space which is the tensor product of two vector spaces. The relationship between the row vectors of the image matrix and that between column vectors can be naturally characterized by the proposed algorithm. The experiments suggest that the proposed algorithm can not only improve the computational efficiency greatly but also achieve much higher recognition accuracies.