# A Notion of Harmonic Clustering in Simplicial Complexes

arXiv: https://arxiv.org/abs/1910.07247 · HTML: https://mlsanity.com/paper/1910.07247/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Dist2Cycle: A Simplicial Neural Network for Homology Localization](https://mlsanity.com/paper/2110.15182/) (2021)
- [The decomposition of the higher-order homology embedding constructed from the k-Laplacian](https://mlsanity.com/paper/2107.10970/) (2021)
- [Topological Point Cloud Clustering](https://mlsanity.com/paper/2303.16716/) (2023)
- [Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal](https://mlsanity.com/paper/2311.14427/) (2023)
- [Point-Level Topological Representation Learning on Point Clouds](https://mlsanity.com/paper/2406.02300/) (2024)
- [Efficient Sparsification of Simplicial Complexes via Local Densities of States](https://mlsanity.com/paper/2502.07558/) (2025)

## Abstract (arXiv)

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.