AAAI Publications, 2009 AAAI Fall Symposium Series

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Learning Topology of Curves with Application to Clustering
Hossein Mobahi, Shankar Rao, Yi Ma

Last modified: 2009-10-30

Abstract


We propose a method for learning the intrinsic topology of a point set sampled from a curve embedded in a high-dimensional ambient space. Our approach does not rely on distances in the ambient space, and thus can recover the topology of sparsely sampled curves, a situation where extant manifold learning methods are expected to fail. We formulate a loss function based on the smoothness of a curve, and derive a greedy procedure for minimizing this loss function. We compare the efficacy of our approach with representative manifold learning and hierarchical clustering methods on both real and synthetic data.

Keywords


Manifold Learning; Curves; Clustering

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