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

Computing and Mathematics

Research output: Book chapter/Published conference paper › Conference 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 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	Korea, Republic of
Period	30/08/10 → 02/09/10

Access to Document

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

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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). Springer. https://doi.org/10.1007/978-3-642-15246-7_26

@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",

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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;

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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.

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

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