A Notion of Harmonic Clustering in Simplicial Complexes

TL;DR

This paper introduces a new clustering method for simplicial complexes that leverages homology and spectral techniques, enabling efficient feature extraction in topological data analysis.

Contribution

It presents a novel, homology-sensitive clustering scheme for simplicial complexes based on spectral methods, with computational efficiency.

Findings

Clustering method is sensitive to the homology of complexes.

Algorithm involves only sparse eigenproblems, ensuring efficiency.

Applicable to topological data analysis for feature extraction.

Abstract

We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of, graph spectral clustering. The algorithm involves only sparse eigenproblems, and is therefore computationally efficient. We believe that it has broad application as a way to extract features from simplicial complexes that often arise in topological data analysis.