<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=undefined&type=result"></script>');
-->
</script>
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.
Accepted at the 40th International Conference on Machine Learning (ICML), 2023. Code available at https://git.rwth-aachen.de/netsci/publication-2023-topological-point-cloud-clustering
Topological Data Analysis, Computational Geometry (cs.CG), Social and Information Networks (cs.SI), FOS: Computer and information sciences, Computer Science - Machine Learning, Spectral Clustering, FOS: Mathematics, Computer Science - Computational Geometry, Algebraic Topology (math.AT), Computer Science - Social and Information Networks, Hodge Laplacian, Mathematics - Algebraic Topology, Machine Learning (cs.LG)
Topological Data Analysis, Computational Geometry (cs.CG), Social and Information Networks (cs.SI), FOS: Computer and information sciences, Computer Science - Machine Learning, Spectral Clustering, FOS: Mathematics, Computer Science - Computational Geometry, Algebraic Topology (math.AT), Computer Science - Social and Information Networks, Hodge Laplacian, Mathematics - Algebraic Topology, Machine Learning (cs.LG)
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 0 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |