Local Canonical Correlation Analysis for Nonlinear Common Variables Discovery

TL;DR

This paper introduces a local CCA-based metric integrated with kernel manifold learning to discover hidden common variables in high-dimensional nonlinear multimodal data without rigid assumptions.

Contribution

It extends CCA to nonlinear settings and combines it with manifold learning for multimodal data analysis, enabling discovery of shared hidden variables.

Findings

Successfully discovers hidden common variables in nonlinear data

Operates without rigid prior model assumptions

Effective in high-dimensional multimodal datasets

Abstract

In this paper, we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high-dimensional observations. We present a metric based on local applications of canonical correlation analysis (CCA) and incorporate it in a kernel-based manifold learning technique.We show that this metric discovers the hidden common variables underlying the multimodal observations by estimating the Euclidean distance between them. Our approach can be viewed both as an extension of CCA to a nonlinear setting as well as an extension of manifold learning to multiple data sets. Experimental results show that our method indeed discovers the common variables underlying high-dimensional nonlinear observations without assuming prior rigid model assumptions.