Clustering in Hilbert simplex geometry

Handle URI:
http://hdl.handle.net/10754/626471
Title:
Clustering in Hilbert simplex geometry
Authors:
Nielsen, Frank; Sun, Ke
Abstract:
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
3-Apr-2017
ARXIV:
arXiv:1704.00454
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1704.00454v2; http://arxiv.org/pdf/1704.00454v2
Appears in Collections:
Other/General Submission; Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorNielsen, Franken
dc.contributor.authorSun, Keen
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2017-04-03en
dc.identifier.urihttp://hdl.handle.net/10754/626471-
dc.description.abstractClustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1704.00454v2en
dc.relation.urlhttp://arxiv.org/pdf/1704.00454v2en
dc.rightsArchived with thanks to arXiven
dc.titleClustering in Hilbert simplex geometryen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionEcole Polytechnique, France and Sony Computer Science Laboratories Inc., Japan.en
dc.identifier.arxividarXiv:1704.00454en
kaust.authorSun, Keen
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