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On the Jensen–Shannon Symmetrization of Distances Relying on Abstract Means

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Nielsen, Frank·2019·Entropy

DOI 10.3390/e21050485PMC PMC7514974

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Abstract

The Jensen–Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback–Leibler divergence which measures the total Kullback–Leibler divergence to the average mixture distribution. However, the Jensen–Shannon divergence between Gaussian distributions is not available in closed form. To bypass this problem, we present a generalization of the Jensen–Shannon (JS) divergence using abstract means which yields closed-form expressions when the mean is chosen according to the parametric family of distributions. More generally, we define the JS-symmetrizations of any distance using parameter mixtures derived from abstract means. In particular, we first show that the geometric mean is well-suited for exponential families, and report two closed-form formula for (i) the geometric Jensen–Shannon divergence between probability densities of the same exponential family; and (ii) the geometric JS-symmetrization of the reverse Kullback–Leibler divergence between probability densities of the same exponential family. As a second illustrating example, we show that the harmonic mean is well-suited for the scale Cauchy distributions, and report a closed-form formula for the harmonic Jensen–Shannon divergence between scale Cauchy distributions. Applications to clustering with respect to these novel Jensen–Shannon divergences are touched upon.

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Generative Adversarial Nets
Labaca-Castro, R. (2023) · Springer eBooks · doi:10.1007/978-3-658-40442-0_9 · Cited by 21,119
Finite Mixture Models
McLachlan, G., & Peel, D. (2000) · Wiley Series in Probability and Statistics · doi:10.1002/0471721182 · Cited by 10,991
Untitled work
(2007) · doi:10.5555/1283383.1283494 · Cited by 7,364
Divergence measures based on the Shannon entropy
Lin, J.-H. (1991) · IEEE Transactions on Information Theory · doi:10.1109/18.61115 · Cited by 5,877
On Measures of Entropy and Information
Rényi, A. (1961) · Project Euclid (Cornell University) · Cited by 4,031
Probability and Measure.
Hawkes, J., & Billingsley, P. (1987) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2982048 · Cited by 1,765
The Minimum Description Length Principle
Grünwald, P. D. (2007) · doi:10.7551/mitpress/4643.001.0001 · Cited by 1,644
Clustering with Bregman Divergences
Banerjee, A., Merugu, S., Dhillon, I. S., & Ghosh, J. (2004) · SIAM International Conference on Data Mining · doi:10.1137/1.9781611972740.22 · Cited by 1,507
Information-type measures of difference of probability distributions and indirect observation
Csiszár, I. (1967) · Studia Scientiarum Mathematicarum Hungarica · Cited by 1,349
Information Geometry and Its Applications
Амари, Ш.-И. (2016) · Applied mathematical sciences · doi:10.1007/978-4-431-55978-8 · Cited by 1,166

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Kafka, 1991, On powers of f-divergences defining a distance, Stud. Sci. Math. Hung., 26, 415
Watanabe, 2004, Kullback information of normal mixture is not an analytic function, IEICE Tech. Rep. Neurocomput., 104, 41
Tzagkarakis, G., and Tsakalides, P. (2004, January 21–23). A statistical approach to texture image retrieval via alpha-stable modeling of wavelet decompositions. Proceedings of the 5th International Workshop on Image Analysis for Multimedia Interactive Services, Instituto Superior Técnico, Lisboa, Portugal.

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Authors: Nielsen, F.
Affiliations: Sony Computer Science Laboratories (JP)
Corresponding author: Nielsen, Frank
ORCID: Nielsen, Frank
Venue: Entropy
Publisher: MDPI AG
Published: 2019-05-11
Volume: 21
Issue: 5
Pages: 485
ISSN: 1099-4300 (ISSN-L)
DOI: 10.3390/e21050485
PMC: PMC7514974
OpenAlex: W3102206498
Cited by: 257
References: 79
Citations by year: 2026: 38 · 2025: 63 · 2024: 40 · 2023: 42 · 2022: 27 · 2021: 30 · 2020: 12 · 2019: 5
FWCI: 8.56
Type: journal article
Language: en
Open access: gold
dx.doi.org
Licence: cc-by
creativecommons.org/licenses/by/4.0/ (vor)
Locations: Entropy (publishedVersion, cc-by)
PubMed Central (publishedVersion, cc-by)
PubMed (publishedVersion)
arXiv (Cornell University) (submittedVersion)
DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
arXiv (Cornell University)
Topics: Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
Physical Sciences › Mathematics › Applied Mathematics › Mathematical Inequalities and Applications
Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
Keywords: Jensen-Shannon divergence, geometric mean, harmonic mean, Kullback-Leibler divergence, exponential family, closed-form expressions, clustering

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