Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach

Area of Science:

• Machine Learning
• Information Theory
• Statistical Analysis

Background:

• Canonical Correlation Analysis (CCA) is a linear method for multi-view data representation learning.
• Nonlinear CCA enhances this by using broader transformations, offering greater power in real-world scenarios.
• The Alternating Conditional Expectation (ACE) algorithm optimally solves nonlinear CCA but faces performance and computational challenges with finite samples.

Purpose of the Study:

• To introduce an information-theoretic compressed representation framework for nonlinear CCA (CRCCA).
• To extend the classical ACE approach by seeking compact data representations that maximize correlation.
• To manage the trade-off between model flexibility and complexity in nonlinear CCA.

Main Methods:

• Developed the Compressed Representation framework for nonlinear CCA (CRCCA).
• Established theoretical bounds and optimality conditions by connecting to rate-distortion theory, information bottleneck, and remote source coding.
• Implemented CRCCA using lattice quantization for a practical solution.

Main Results:

• CRCCA offers a controlled trade-off between model flexibility and complexity.
• The framework provides soft dimensionality reduction based on mutual information.
• Theoretical connections to established information-theoretic concepts were established.

Conclusions:

• CRCCA provides a novel, information-theoretic approach to nonlinear CCA.
• The framework offers improved performance and computational efficiency over traditional methods.
• CRCCA enables effective dimensionality reduction and balances model complexity with representational power.