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Matrix-Variate Probabilistic Model for Canonical Correlation Analysis

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.

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Correspondence to Mehran Safayani.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Safayani, M., Manzuri Shalmani, M.T. Matrix-Variate Probabilistic Model for Canonical Correlation Analysis. EURASIP J. Adv. Signal Process. 2011, 748430 (2011). https://doi.org/10.1155/2011/748430

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Keywords

  • Parameter Estimation
  • Information Technology
  • Computer Vision
  • Discriminant Analysis
  • Original Image