Clustering in Hilbert’s Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices

DOI10.1007/978-3-030-02520-5_11zbMath1418.53022arXiv1704.00454OpenAlexW2901691022MaRDI QIDQ4967762

Ke Sun, Frank Nielsen

Publication date: 10 July 2019

Published in: Geometric Structures of Information (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.00454

zbMATH Keywords

Finsler geometryinformation geometry\(k\)-means clusteringelliptope\(k\)-center clusteringFisher-Riemannian geometryHilbert simplex geometrymultinoulli distributionpolytope distance

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) General theory of linear incidence geometry and projective geometries (51A05) Local Riemannian geometry (53B20) Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (51M35)

Related Items (4)

Theoretically and Computationally Convenient Geometries on Full-Rank Correlation Matrices ⋮ Anomaly detection in the probability simplex under different geometries ⋮ Geodesics and curvature of the quotient-affine metrics on full-rank correlation matrices ⋮ cCorrGAN: conditional correlation GAN for learning empirical conditional distributions in the elliptope

Uses Software

• PMTK

Cites Work

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