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


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.


Manifold Learning; Curves; Clustering

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