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Representational Rényi Heterogeneity.

Abraham Nunes1,2, Martin Alda1, Timothy Bardouille3

  • 1Department of Psychiatry, Dalhousie University, Halifax, NS B3H 2E2, Canada.

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

We introduce representational Rényi heterogeneity (RRH) to measure system diversity without predefined categories. This new method offers a flexible approach for analyzing complex data, applicable across various scientific fields.

Keywords:
Hill numbersLeinster–Cobbold IndexRao’s quadratic entropyRényi heterogeneitydiversityfunctional diversity indicesheterogeneityrepresentation learningvariational autoencoder

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Area of Science:

  • Complexity Science
  • Information Theory
  • Ecology
  • Economics

Background:

  • Rényi heterogeneity indices (Hill numbers) quantify discrete system diversity.
  • Existing methods require predefined categories and distance metrics, limiting their application to complex, non-categorical data.

Purpose of the Study:

  • Introduce representational Rényi heterogeneity (RRH) for measuring diversity in systems with ill-defined categories.
  • Develop a method applicable to abstract representations learned from data, overcoming limitations of traditional heterogeneity measures.

Main Methods:

  • Transform observable data into a latent space where heterogeneity is computed.
  • RRH requires no a priori binning or definition of distance functions on the observable space.
  • Demonstrated RRH on beta-mixture distributions and abstract representations from deep neural networks.

Main Results:

  • RRH generalizes existing biodiversity and economic equality indices.
  • RRH shows improved responsiveness to changes in mixture component separation and weighting compared to existing indices.
  • Successfully measured RRH in natural images using deep learning-derived representations.

Conclusions:

  • RRH provides a robust and flexible framework for heterogeneity measurement across diverse scientific disciplines.
  • Enables heterogeneity analysis in fields where data does not fit traditional index assumptions.
  • Advances the application of diversity metrics to complex, abstract, and high-dimensional data.