Consistent Manifold Representation for Topological Data Analysis

7 Jun 2016Tyrus BerryTimothy Sauer

For data sampled from an arbitrary density on a manifold embedded in Euclidean space, we introduce the Continuous k-Nearest Neighbors (CkNN) graph construction. We prove that CkNN is the unique unweighted construction that is consistent with the connected components of the underlying manifold in the limit of large data, for compact Riemannian manifolds and a large class of non-compact manifolds... (read more)

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