A Notion of Harmonic Clustering in Simplicial Complexes
This provides a method for extracting features in topological data analysis, but it appears incremental as an extension of graph spectral clustering to higher dimensions.
The paper tackles the problem of clustering simplices in simplicial complexes by introducing a novel scheme sensitive to homology, inspired by graph spectral clustering, and reports computational efficiency through sparse eigenproblems.
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.