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Common Information Components Analysis.

Erixhen Sula1, Michael Gastpar1

  • 1School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

Entropy (Basel, Switzerland)
|February 3, 2021
PubMed
Summary

Common Information Components Analysis (CICA) extracts features by quantifying commonality between variables. This novel method generalizes Canonical Correlation Analysis (CCA) and extends to multiple datasets.

Keywords:
CCAcanonical correlation analysiscommon informationdimensionality reductionfeature extractionunsupervised

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Area of Science:

  • Information Theory
  • Statistical Learning
  • Data Analysis

Background:

  • Wyner's common information quantifies shared information between random variables.
  • Existing methods may lack flexibility in feature extraction based on common information.

Purpose of the Study:

  • Introduce Common Information Components Analysis (CICA) for novel feature construction.
  • Establish a rigorous connection between information theory and Canonical Correlation Analysis (CCA).
  • Generalize CCA and extend feature extraction to multiple datasets.

Main Methods:

  • A two-step procedure involving extraction of Wyner's common information.
  • Back-projection of common information onto original variables to create features.
  • Utilizing a free parameter γ to control feature complexity.

Main Results:

  • CICA precisely reduces to Canonical Correlation Analysis (CCA) for Gaussian data.
  • The parameter γ in CICA determines the number of extracted CCA components.
  • Demonstrated CICA's capability for feature extraction beyond two datasets.

Conclusions:

  • CICA offers a generalized framework for feature extraction rooted in information theory.
  • Provides a novel, rigorous link between common information measures and CCA.
  • Presents a flexible and extensible method for analyzing complex data structures.