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Nonlinear Canonical Correlation Analysis:A Compressed Representation Approach.

Amichai Painsky1, Meir Feder2, Naftali Tishby3

  • 1The Industrial Engineering Department, Tel Aviv University, Tel Aviv 6997801, Israel.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We introduce a compressed representation framework for nonlinear Canonical Correlation Analysis (CCA) to improve performance and reduce computational load. This information-theoretic approach balances model flexibility and complexity for better multi-view data analysis.

Keywords:
alternating conditional expectationcanonical correlation analysisdimensionality reductioninformation bottleneckremote source coding

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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.