A latent variable model for two-dimensional canonical correlation analysis and the variational inference
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A latent variable model for two-dimensional canonical correlation analysis and the variational inference Mehran Safayani1 · Saeid Momenzadeh1 · Abdolreza Mirzaei1 · Masoomeh Sadat Razavi1 Published online: 6 April 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. Keywords Canonical correlation analysis · Probabilistic dimension reduction · Matrix-variate distribution · Variational expectation maximization
1 Introduction Dimension reduction is one of the essential steps in the data mining process, which makes data analyses easier and faster for the learning algorithms. Canonical correlation analysis (CCA) is a well-known technique for the multi-view data dimension reduction. Bach and Jordan (2005) presented Communicated by A. Di Nola.
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Mehran Safayani [email protected] Saeid Momenzadeh [email protected] Abdolreza Mirzaei [email protected] Masoomeh Sadat Razavi [email protected]
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Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
probabilistic interpretation of CCA and named it the probabilistic CCA (PCCA). Recently, these have become a major focus among researches in this fields (Ju et al. 2018, 2016; Ju et al. 2015) and are very advantageous in handling of missing and outlier data (Chen et al. 2009), auto
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