Topological Point Cloud Clustering

• URL: http://arxiv.org/abs/2303.16716v3
• Date: Sat, 01 Mar 2025 12:21:38 GMT
• Title: Topological Point Cloud Clustering
• Authors: Vincent P. Grande, Michael T. Schaub,
• Abstract summary: Topological Point Cloud Clustering (TPCC) is a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features.<n>We test TPCC on both synthetic and real-world data and compare it with classical spectral clustering.
• Score: 5.079602839359521
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Scalable Context-Preserving Model-Aware Deep Clustering for Hyperspectral Images [51.95768218975529]
  Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs)<n>Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a self-representation matrix with complexity of O(n2), followed by spectral clustering.<n>We propose a scalable, context-preserving deep clustering method based on basis representation, which jointly captures local and non-local structures for efficient HSI clustering.
  arXiv  Detail & Related papers  (2025-06-12T16:43:09Z)
• Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration [14.904264782690639]
  Clustering complex datasets containing intertwined shapes poses significant challenges.<n>We introduce the concept of the Betti sequences to capture flexibly essential features from the topological structures.<n>Our proposed algorithm is adept at clustering complex, intertwined shapes contained in the datasets.
  arXiv  Detail & Related papers  (2025-05-07T11:46:02Z)
• Node-Level Topological Representation Learning on Point Clouds [5.079602839359521]
  We propose a novel method to extract node-level topological features from complex point clouds. We verify the effectiveness of these topological point features on both synthetic and real-world data.
  arXiv  Detail & Related papers  (2024-06-04T13:29:12Z)
• Datacube segmentation via Deep Spectral Clustering [76.48544221010424]
  Extended Vision techniques often pose a challenge in their interpretation. The huge dimensionality of data cube spectra poses a complex task in its statistical interpretation. In this paper, we explore the possibility of applying unsupervised clustering methods in encoded space. A statistical dimensional reduction is performed by an ad hoc trained (Variational) AutoEncoder, while the clustering process is performed by a (learnable) iterative K-Means clustering algorithm.
  arXiv  Detail & Related papers  (2024-01-31T09:31:28Z)
• Variational Quantum Approximated Spectral Clustering [0.6718184400443239]
  We propose Variational Quantum Approximated Spectral Clustering (VQASC), which extends quantum distance-based classifier models to the clustering framework. Our approach uses efficient quantum circuit designs whose depth scales sub-quadratically with dataset size, enabling the computation of weighted sums over various matrix representations of an undirected graph.
  arXiv  Detail & Related papers  (2023-09-08T17:54:42Z)
• Instance-Optimal Cluster Recovery in the Labeled Stochastic Block Model [79.46465138631592]
  We devise an efficient algorithm that recovers clusters using the observed labels. We present Instance-Adaptive Clustering (IAC), the first algorithm whose performance matches these lower bounds both in expectation and with high probability.
  arXiv  Detail & Related papers  (2023-06-18T08:46:06Z)
• Enhancing cluster analysis via topological manifold learning [0.3823356975862006]
  We show that inferring the topological structure of a dataset before clustering can considerably enhance cluster detection. We combine manifold learning method UMAP for inferring the topological structure with density-based clustering method DBSCAN.
  arXiv  Detail & Related papers  (2022-07-01T15:53:39Z)
• flow-based clustering and spectral clustering: a comparison [0.688204255655161]
  We study a novel graph clustering method for data with an intrinsic network structure. We exploit an intrinsic network structure of data to construct Euclidean feature vectors. Our results indicate that our clustering methods can cope with certain graph structures.
  arXiv  Detail & Related papers  (2022-06-20T21:49:52Z)
• Perfect Spectral Clustering with Discrete Covariates [68.8204255655161]
  We propose a spectral algorithm that achieves perfect clustering with high probability on a class of large, sparse networks. Our method is the first to offer a guarantee of consistent latent structure recovery using spectral clustering.
  arXiv  Detail & Related papers  (2022-05-17T01:41:06Z)
• Fast and explainable clustering based on sorting [0.0]
  We introduce a fast and explainable clustering method called CLASSIX. The algorithm is controlled by two scalar parameters, namely a distance parameter for the aggregation and another parameter controlling the minimal cluster size. Our experiments demonstrate that CLASSIX competes with state-of-the-art clustering algorithms.
  arXiv  Detail & Related papers  (2022-02-03T08:24:21Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations. We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• Self-supervised Contrastive Attributed Graph Clustering [110.52694943592974]
  We propose a novel attributed graph clustering network, namely Self-supervised Contrastive Attributed Graph Clustering (SCAGC) In SCAGC, by leveraging inaccurate clustering labels, a self-supervised contrastive loss, are designed for node representation learning. For the OOS nodes, SCAGC can directly calculate their clustering labels.
  arXiv  Detail & Related papers  (2021-10-15T03:25:28Z)
• Scalable Hierarchical Agglomerative Clustering [65.66407726145619]
  Existing scalable hierarchical clustering methods sacrifice quality for speed. We present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points.
  arXiv  Detail & Related papers  (2020-10-22T15:58:35Z)
• Stable and consistent density-based clustering via multiparameter persistence [77.34726150561087]
  We consider the degree-Rips construction from topological data analysis. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance. We integrate these methods into a pipeline for density-based clustering, which we call Persistable.
  arXiv  Detail & Related papers  (2020-05-18T19:45:04Z)
• Robust spectral clustering using LASSO regularization [0.0]
  This paper presents a variant of spectral clustering, called 1-spectral clustering, performed on a new random model closely related to block model. Its goal is to promote a sparse eigenbasis solution of a 1 minimization problem revealing the natural structure of the graph.
  arXiv  Detail & Related papers  (2020-04-08T07:12:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.