# Power Weighted Shortest Paths for Clustering Euclidean Data

arXiv: https://arxiv.org/abs/1905.13345 · HTML: https://mlsanity.com/paper/1905.13345/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 10 of 10)

- [Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms](https://mlsanity.com/paper/2307.05750/) (2023)
- [Learning Distances from Data with Normalizing Flows and Score Matching](https://mlsanity.com/paper/2407.09297/) (2024)
- [Graph-based Semi-supervised Local Clustering with Few Labeled Nodes](https://mlsanity.com/paper/2211.11114/) (2022)
- [Choosing the parameter of the Fermat distance: navigating geometry and noise](https://mlsanity.com/paper/2311.18663/) (2023)
- [Geodesic Calculus on Implicitly Defined Latent Manifolds](https://mlsanity.com/paper/2510.09468/) (2025)
- [Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphs](https://mlsanity.com/paper/2603.26940/) (2026)
- [High-dimensional Semi-supervised Classification via the Fermat Distance](https://mlsanity.com/paper/2604.23573/) (2026)
- [Preprocessing power weighted shortest path data using a s-Well Separated Pair Decomposition](https://mlsanity.com/paper/2103.11216/) (2021)
- [K-means with learned metrics](https://mlsanity.com/paper/2603.14601/) (2026)
- [Fermat Active Laplace Learning for Semi-Supervised Hyperspectral Image Classification](https://mlsanity.com/paper/2608.02483/) (2026)

## Abstract (arXiv)

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.