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 |
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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 | |
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 |
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Country/Territory | Korea, Republic of |
Period | 30/08/10 → 02/09/10 |