Power Weighted Shortest Paths for Clustering Euclidean Data

Abstract

We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also present a fast algorithm for computing these distances.

24 pages. Final version. To appear in Foundations of Data Science