Matrix-Variate Probabilistic Model for Canonical Correlation Analysis

Motivated by the fact that in computer vision data samples are matrices, in this paper, we propose a matrix-variate probabilistic model for canonical correlation analysis (CCA). Unlike probabilistic CCA which converts the image samples into the vectors, our method uses the original image matrices for data representation. We show that the maximum likelihood parameter estimation of the model leads to the two-dimensional canonical correlation directions. This model helps for better understanding of two-dimensional Canonical Correlation Analysis (2DCCA), and for further extending the method into more complex probabilistic model. In addition, we show that two-dimensional Linear Discriminant Analysis (2DLDA) can be obtained as a special case of 2DCCA.