Clustering and dimensionality reduction on Riemannian manifolds

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Clustering and dimensionality reduction on Riemannian manifolds
We propose a novel algorithm for clustering data sampled from multiple submanifolds of a Riemannian manifold. First, we learn a representation of the data using generalizations of local nonlinear dimensionality reduction algorithms from Euclidean to Riemannian spaces. Such generalizations exploit geometric properties of the Riemannian space, particularly its Riemannian metric. Then, assuming that the data points from different groups are separated, we show that the null space of a matrix built from the local representation gives the segmentation of the data. Our method is computationally simple and performs automatic segmentation without requiring user initialization. We present results on 2-D motion segmentation and diffusion tensor imaging segmentation.
Alvina Goh, René Vidal
Added 12 Oct 2009
Updated 28 Oct 2009
Type Conference
Year 2008
Where CVPR
Authors Alvina Goh, René Vidal
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