Geometric MedianShift over Riemannian Manifolds

Authors: Yang Wang Xiaodi Huang

Publish Date: 2010/8/30

Volume: , Issue: , Pages: 268-279

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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 On 2 compared to On 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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