Dimensionality, granularity, and differential residual weighted entropy

Tunnicliffe, Martin and Hunter, Gordon (2019) Dimensionality, granularity, and differential residual weighted entropy. Entropy, 21(9), p. 825. ISSN (online) 1099-4300

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While Shannon’s differential entropy adequately quantifies a dimensioned random variable’s information deficit under a given measurement system, the same cannot be said of differential weighted entropy in its existing formulation. We develop weighted and residual weighted entropies of a dimensioned quantity from their discrete summation origins, exploring the relationship between their absolute and differential forms, and thus derive a “differentialized” absolute entropy based on a chosen “working granularity” consistent with Buckingham’s Π-theorem. We apply this formulation to three common continuous distributions: exponential, Gaussian, and gamma and consider policies for optimizing the working granularity.

Item Type: Article
Research Area: Applied mathematics
Computer science and informatics
Electrical and electronic engineering
Statistics and operational research
Faculty, School or Research Centre: Faculty of Science, Engineering and Computing
Faculty of Science, Engineering and Computing > School of Computer Science and Mathematics
Depositing User: Katrina Clifford
Date Deposited: 05 Sep 2019 10:14
Last Modified: 05 Sep 2019 12:52
DOI: https://doi.org/10.3390/e21090825
URI: http://eprints.kingston.ac.uk/id/eprint/43840

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