Geometric Median-Shift over Riemannian Manifolds

Yang Wang, Xiaodi Huang

Research output: Book chapter/Published conference paperConference paper

3 Citations (Scopus)

Abstract

Manifold clustering finds wide applications in many areas. In this paper, we propose a new kernel function that makes use of Riemannian geodesic distances among data points, and present a Geometric median shift algorithm over Riemannian Manifolds. Relying on the geometric median shift, together with geodesic distances, our approach is able to effectively cluster data points distributed over Riemannian manifolds. In addition to improving the clustering results, the complexity for calculating geometric median is reduced to O(n 2), compared to O(n 2logn 2) for Tukey median. Using both Riemannian Manifolds and Euclidean spaces, we compare the geometric median shift and mean shift algorithms for clustering synthetic and real data sets.
Original languageEnglish
Title of host publicationPRICAI 2010
Subtitle of host publicationTrends in Artificial Intelligence.
EditorsByoung-Tak Zhang, Mehmet A Orgun
Place of PublicationGermany
PublisherSpringer
Pages268-279
Number of pages12
Volume6230
DOIs
Publication statusPublished - 2010
EventPacific Rim International Conference on Artificial Intelligence - Daegu, Korea, Korea, Republic of
Duration: 30 Aug 201002 Sep 2010

Conference

ConferencePacific Rim International Conference on Artificial Intelligence
CountryKorea, Republic of
Period30/08/1002/09/10

Cite this

Wang, Y., & Huang, X. (2010). Geometric Median-Shift over Riemannian Manifolds. In B-T. Zhang, & M. A. Orgun (Eds.), PRICAI 2010: Trends in Artificial Intelligence. (Vol. 6230, pp. 268-279). Germany: Springer. https://doi.org/10.1007/978-3-642-15246-7_26
Wang, Yang ; Huang, Xiaodi. / Geometric Median-Shift over Riemannian Manifolds. PRICAI 2010: Trends in Artificial Intelligence.. editor / Byoung-Tak Zhang ; Mehmet A Orgun. Vol. 6230 Germany : Springer, 2010. pp. 268-279
@inproceedings{2acb6450cb9642e6b375fc99d78ba79f,
title = "Geometric Median-Shift over Riemannian Manifolds",
abstract = "Manifold clustering finds wide applications in many areas. In this paper, we propose a new kernel function that makes use of Riemannian geodesic distances among data points, and present a Geometric median shift algorithm over Riemannian Manifolds. Relying on the geometric median shift, together with geodesic distances, our approach is able to effectively cluster data points distributed over Riemannian manifolds. In addition to improving the clustering results, the complexity for calculating geometric median is reduced to O(n 2), compared to O(n 2logn 2) for Tukey median. Using both Riemannian Manifolds and Euclidean spaces, we compare the geometric median shift and mean shift algorithms for clustering synthetic and real data sets.",
author = "Yang Wang and Xiaodi Huang",
note = "Imported on 03 May 2017 - DigiTool details were: publisher = Germany: Springer, 2010. editor/s (773b) = Byoung-Tak Zhang and Mehmet A Orgun; Event dates (773o) = 30-08-2010-02-09-2010; Parent title (773t) = Pacific Rim International Conference on Artificial Intelligence. ISSNs: 0302-9743;",
year = "2010",
doi = "10.1007/978-3-642-15246-7_26",
language = "English",
volume = "6230",
pages = "268--279",
editor = "Byoung-Tak Zhang and Orgun, {Mehmet A}",
booktitle = "PRICAI 2010",
publisher = "Springer",
address = "United States",

}

Wang, Y & Huang, X 2010, Geometric Median-Shift over Riemannian Manifolds. in B-T Zhang & MA Orgun (eds), PRICAI 2010: Trends in Artificial Intelligence.. vol. 6230, Springer, Germany, pp. 268-279, Pacific Rim International Conference on Artificial Intelligence, Korea, Republic of, 30/08/10. https://doi.org/10.1007/978-3-642-15246-7_26

Geometric Median-Shift over Riemannian Manifolds. / Wang, Yang; Huang, Xiaodi.

PRICAI 2010: Trends in Artificial Intelligence.. ed. / Byoung-Tak Zhang; Mehmet A Orgun. Vol. 6230 Germany : Springer, 2010. p. 268-279.

Research output: Book chapter/Published conference paperConference paper

TY - GEN

T1 - Geometric Median-Shift over Riemannian Manifolds

AU - Wang, Yang

AU - Huang, Xiaodi

N1 - Imported on 03 May 2017 - DigiTool details were: publisher = Germany: Springer, 2010. editor/s (773b) = Byoung-Tak Zhang and Mehmet A Orgun; Event dates (773o) = 30-08-2010-02-09-2010; Parent title (773t) = Pacific Rim International Conference on Artificial Intelligence. ISSNs: 0302-9743;

PY - 2010

Y1 - 2010

N2 - Manifold clustering finds wide applications in many areas. In this paper, we propose a new kernel function that makes use of Riemannian geodesic distances among data points, and present a Geometric median shift algorithm over Riemannian Manifolds. Relying on the geometric median shift, together with geodesic distances, our approach is able to effectively cluster data points distributed over Riemannian manifolds. In addition to improving the clustering results, the complexity for calculating geometric median is reduced to O(n 2), compared to O(n 2logn 2) for Tukey median. Using both Riemannian Manifolds and Euclidean spaces, we compare the geometric median shift and mean shift algorithms for clustering synthetic and real data sets.

AB - Manifold clustering finds wide applications in many areas. In this paper, we propose a new kernel function that makes use of Riemannian geodesic distances among data points, and present a Geometric median shift algorithm over Riemannian Manifolds. Relying on the geometric median shift, together with geodesic distances, our approach is able to effectively cluster data points distributed over Riemannian manifolds. In addition to improving the clustering results, the complexity for calculating geometric median is reduced to O(n 2), compared to O(n 2logn 2) for Tukey median. Using both Riemannian Manifolds and Euclidean spaces, we compare the geometric median shift and mean shift algorithms for clustering synthetic and real data sets.

U2 - 10.1007/978-3-642-15246-7_26

DO - 10.1007/978-3-642-15246-7_26

M3 - Conference paper

VL - 6230

SP - 268

EP - 279

BT - PRICAI 2010

A2 - Zhang, Byoung-Tak

A2 - Orgun, Mehmet A

PB - Springer

CY - Germany

ER -

Wang Y, Huang X. Geometric Median-Shift over Riemannian Manifolds. In Zhang B-T, Orgun MA, editors, PRICAI 2010: Trends in Artificial Intelligence.. Vol. 6230. Germany: Springer. 2010. p. 268-279 https://doi.org/10.1007/978-3-642-15246-7_26