  Describing the dimension reduction (DR) techniques by means of probabilistic
models has recently been given special attention. Probabilistic models, in
addition to a better interpretability of the DR methods, provide a framework
for further extensions of such algorithms. One of the new approaches to the
probabilistic DR methods is to preserving the internal structure of data. It is
meant that it is not necessary that the data first be converted from the matrix
or tensor format to the vector format in the process of dimensionality
reduction. In this paper, a latent variable model for matrix-variate data for
canonical correlation analysis (CCA) is proposed. Since in general there is not
any analytical maximum likelihood solution for this model, we present two
approaches for learning the parameters. The proposed methods are evaluated
using the synthetic data in terms of convergence and quality of mappings. Also,
real data set is employed for assessing the proposed methods with several
probabilistic and none-probabilistic CCA based approaches. The results confirm
the superiority of the proposed methods with respect to the competing
algorithms. Moreover, this model can be considered as a framework for further
extensions.
