Representational renyi heterogeneity

Abraham Nunes, Martin Alda, Timothy Bardouille, Thomas Trappenberg

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5 Citas (Scopus)

Resumen

Adiscrete system's heterogeneity ismeasured by the Renyi heterogeneity family of indices (also known as Hill numbers or Hannah-Kay indices), whose units are the numbers equivalent. Unfortunately, numbers equivalent heterogeneity measures for non-categorical data require a priori (A) categorical partitioning and (B) pairwise distance measurement on the observable data space, thereby precluding application to problems with ill-defined categories or where semantically relevant features must be learned as abstractions from some data. We thus introduce representational Renyi heterogeneity (RRH), which transforms an observable domain onto a latent space upon which the Renyi heterogeneity is both tractable and semantically relevant. This method requires neither a priori binning nor definition of a distance function on the observable space. We show that RRH can generalize existing biodiversity and economic equality indices. Compared with existing indices on a beta-mixture distribution, we show that RRH responds more appropriately to changes in mixture component separation and weighting. Finally, we demonstrate the measurement of RRH in a set of natural images, with respect to abstract representations learned by a deep neural network. The RRH approach will further enable heterogeneity measurement in disciplines whose data do not easily conform to the assumptions of existing indices.

Idioma originalEnglish
Número de artículo417
PublicaciónEntropy
Volumen22
N.º4
DOI
EstadoPublished - abr. 1 2020

Nota bibliográfica

Funding Information:
This research was funded by Genome Canada (A.N., M.A.), the Nova Scotia Health Research Foundation (A.N.), the Killam Trusts (A.N.), and the Ruth Wagner Memorial Fund (A.N.).

Funding Information:
Funding: This research was funded by Genome Canada (A.N., M.A.), the Nova Scotia Health Research Foundation (A.N.), the Killam Trusts (A.N.), and the Ruth Wagner Memorial Fund (A.N.).

Publisher Copyright:
© 2020 by the authors.

ASJC Scopus Subject Areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering

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