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 original | English |
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Número de artículo | 417 |
Publicación | Entropy |
Volumen | 22 |
N.º | 4 |
DOI | |
Estado | Published - 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