A Latent Variable Model for Two-Dimensional Canonical Correlation Analysis and its Variational Inference

TL;DR

This paper introduces a probabilistic latent variable model for two-dimensional canonical correlation analysis (CCA) that preserves data structure, offers interpretability, and demonstrates superior performance over existing methods through synthetic and real data evaluations.

Contribution

It proposes a novel probabilistic model for matrix-variate data in CCA, along with two parameter learning approaches, enhancing data structure preservation and interpretability.

Findings

Proposed methods outperform existing CCA algorithms on synthetic data.

The models show superior convergence and mapping quality.

Real data experiments confirm the effectiveness of the new approaches.

Abstract

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.