Abstract
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.
Highlights
A probabilistic interpretation of statistical dimension reduction algorithms has been proposed by several authors
We show that the estimating the parameters of the proposed model leads to the twodimensional canonical correlation analysis directions
Conventional probabilistic model only works for vectors data while the data samples in computer vision applications are matrices
Summary
A probabilistic interpretation of statistical dimension reduction algorithms has been proposed by several authors. Some statistical methods that directly perform on the image matrices without the image to vector conversion procedure have been proposed These methods make use of EURASIP Journal on Advances in Signal Processing t1 x t2 Figure 1: Probabilistic graphical model for CCA. Because of the success of the matrix-based methods, recently some researchers have developed probabilistic model for matrix and tensor extensions of PCA [21,22,23,24]. They do not show the maximum likelihood relationship between their models and corresponding PCA.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
