Topological Point Cloud Clustering
This method addresses clustering challenges in point cloud data, potentially benefiting fields like computer vision or data analysis, but it appears incremental as it combines existing techniques.
The authors tackled the problem of clustering points in arbitrary point clouds by developing Topological Point Cloud Clustering (TPCC), which integrates spectral clustering with topological data analysis to leverage richer topological features, and they tested it on synthetic and real-world data, comparing it to classical spectral clustering.
We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering.