Point-Level Topological Representation Learning on Point Clouds

Vincent Peter Grande, Michael T Schaub
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:20368-20398, 2025.

Abstract

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise and heterogeneous sampling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-grande25a, title = {Point-Level Topological Representation Learning on Point Clouds}, author = {Grande, Vincent Peter and Schaub, Michael T}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {20368--20398}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/grande25a/grande25a.pdf}, url = {https://proceedings.mlr.press/v267/grande25a.html}, abstract = {Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise and heterogeneous sampling.} }
Endnote
%0 Conference Paper %T Point-Level Topological Representation Learning on Point Clouds %A Vincent Peter Grande %A Michael T Schaub %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-grande25a %I PMLR %P 20368--20398 %U https://proceedings.mlr.press/v267/grande25a.html %V 267 %X Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise and heterogeneous sampling.
APA
Grande, V.P. & Schaub, M.T.. (2025). Point-Level Topological Representation Learning on Point Clouds. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:20368-20398 Available from https://proceedings.mlr.press/v267/grande25a.html.

Related Material