# Power Weighted Shortest Paths for Clustering Euclidean Data

## TL;DR

This paper introduces power weighted shortest path distances for clustering high-dimensional Euclidean data, demonstrating improved accuracy and providing an efficient algorithm for computation.

## Contribution

It proposes a novel distance function for clustering that leverages power weights, with theoretical justification and a fast algorithm for practical use.

## Key findings

- Higher clustering accuracy with power weighted shortest paths
- Theoretical support for the effectiveness of the method
- Efficient algorithm for computing the distances

## 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.