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dc.contributor.authorNielsen, Frank
dc.contributor.authorSun, Ke
dc.contributor.authorMarchand-Maillet, Stephane
dc.date.accessioned2017-06-05T06:02:24Z
dc.date.available2017-06-05T06:02:24Z
dc.date.issued2017-03-16
dc.identifier.citationNielsen F, Sun K, Marchand-Maillet S (2017) On Hölder Projective Divergences. Entropy 19: 122. Available: http://dx.doi.org/10.3390/e19030122.
dc.identifier.issn1099-4300
dc.identifier.doi10.3390/e19030122
dc.identifier.urihttp://hdl.handle.net/10754/624040
dc.description.abstractWe describe a framework to build distances by measuring the tightness of inequalities and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Holder ordinary and reverse inequalities and present two novel classes of Holder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy-Schwarz divergence. We report closed-form formulas for those statistical dissimilarities when considering distributions belonging to the same exponential family provided that the natural parameter space is a cone (e.g., multivariate Gaussians) or affine (e.g., categorical distributions). Those new classes of Holder distances are invariant to rescaling and thus do not require distributions to be normalized. Finally, we show how to compute statistical Holder centroids with respect to those divergences and carry out center-based clustering toy experiments on a set of Gaussian distributions which demonstrate empirically that symmetrized Holder divergences outperform the symmetric Cauchy-Schwarz divergence.
dc.description.sponsorshipThe authors gratefully thank the referees for their comments. Ke Sun is funded by King Abdullah University of Science and Technology (KAUST).
dc.publisherMDPI AG
dc.relation.urlhttp://www.mdpi.com/1099-4300/19/3/122
dc.rightsThis is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectHolder inequalities
dc.subjectHolder divergences
dc.subjectprojective divergences
dc.subjectCauchy-Schwarz divergence
dc.subjectHolder escort divergences
dc.subjectskew Bhattacharyya divergences
dc.subjectexponential families
dc.subjectconic exponential families
dc.subjectescort distribution
dc.subjectclustering
dc.titleOn Hölder Projective Divergences
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalEntropy
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionComputer Science Department LIX, École Polytechnique, 91128 Palaiseau Cedex, France
dc.contributor.institutionSony Computer Science Laboratories Inc., Tokyo 141-0022, Japan
dc.contributor.institutionComputer Vision and Multimedia Laboratory (Viper), University of Geneva, CH-1211 Geneva, Switzerland
dc.identifier.arxivid1701.03916
kaust.personSun, Ke
refterms.dateFOA2018-06-13T18:17:22Z


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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Except where otherwise noted, this item's license is described as This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).