RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds
- Others:
- Understanding the Shape of Data (DATASHAPE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)
- Laboratoire d'Informatique Gaspard-Monge (LIGM) ; École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel
- The University of Tokyo (UTokyo)
- Fujitsu Laboratories of America, Inc., Sunnyvale CA
- ANR-19-CHIA-0001,TopAI,TopAI : Analyse Topologique des Données pour l'apprentissage et l'IA(2019)
Citation
Description
The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in applications is often hindered by two major limitations: the computational complexity required to compute such descriptors exactly, and their sensitivity to even low-level proportions of outliers. In this work, we propose to bypass these two burdens in a data-driven setting by entrusting the estimation of (vectorization of) PDs built on top of point clouds to a neural network architecture that we call RipsNet. Once trained on a given data set, RipsNet can estimate topological descriptors on test data very efficiently with generalization capacity. Furthermore, we prove that RipsNet is robust to input perturbations in terms of the 1-Wasserstein distance, a major improvement over the standard computation of PDs that only enjoys Hausdorff stability, yielding RipsNet to substantially outperform exactly-computed PDs in noisy settings. We showcase the use of RipsNet on both synthetic and real-world data. Our open-source implementation is publicly available at https://github.com/hensel-f/ripsnet and will be included in the Gudhi library.
Abstract
23 pages, 4 figures
Additional details
- URL
- https://hal.inria.fr/hal-03560450
- URN
- urn:oai:HAL:hal-03560450v1
- Origin repository
- UNICA