Geometric median-shift over Riemannian manifolds

Authors:
Yang Wang;Xiaodi Huang
Affiliations:
School of Computer Science and Technology, Tianjin University, Tianjin, China;School of Computing and Mathematics, Charles Sturt University, Albury, NSW, Australia
Venue:
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Year:
2010

Citing 6
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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(n2), compared to O(n2 log n2) 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.