Geometric Median-Shift over Riemannian Manifolds

Yang Wang; Xiaodi Huang

doi:10.1007/978-3-642-15246-7_26

Geometric Median-Shift over Riemannian Manifolds

Yang Wang, Xiaodi Huang

Research output: Book chapter/Published conference paper › Conference paper › peer-review

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 language	English
Title of host publication	PRICAI 2010
Subtitle of host publication	Trends in Artificial Intelligence.
Editors	Byoung-Tak Zhang, Mehmet A Orgun
Place of Publication	Germany
Publisher	Springer
Pages	268-279
Number of pages	12
Volume	6230
DOIs	https://doi.org/10.1007/978-3-642-15246-7_26
Publication status	Published - 2010
Event	Pacific Rim International Conference on Artificial Intelligence - Daegu, Korea, Korea, Republic of Duration: 30 Aug 2010 → 02 Sep 2010

Conference

Conference	Pacific Rim International Conference on Artificial Intelligence
Country/Territory	Korea, Republic of
Period	30/08/10 → 02/09/10

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

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@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; ; Pacific Rim International Conference on Artificial Intelligence ; Conference date: 30-08-2010 Through 02-09-2010",

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",

}

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

T2 - Pacific Rim International Conference on Artificial Intelligence

Y2 - 30 August 2010 through 2 September 2010

ER -

Geometric Median-Shift over Riemannian Manifolds

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