Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Carriere, Mathieu"'
We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g., manifold learning
Externí odkaz:
http://arxiv.org/abs/2408.01379
Publikováno v:
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:43986-44011, 2024
Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-value
Externí odkaz:
http://arxiv.org/abs/2406.07224
Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some topologic
Externí odkaz:
http://arxiv.org/abs/2405.18820
Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which is a combin
Externí odkaz:
http://arxiv.org/abs/2402.12854
A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\
Externí odkaz:
http://arxiv.org/abs/2306.11170
Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case --
Externí odkaz:
http://arxiv.org/abs/2306.03801
Autor:
Arnal, Charles, Hensel, Felix, Carrière, Mathieu, Lacombe, Théo, Kurihara, Hiroaki, Ike, Yuichi, Chazal, Frédéric
Despite their successful application to a variety of tasks, neural networks remain limited, like other machine learning methods, by their sensitivity to shifts in the data: their performance can be severely impacted by differences in distribution bet
Externí odkaz:
http://arxiv.org/abs/2305.13271
In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when
Externí odkaz:
http://arxiv.org/abs/2206.02026
Autor:
de Surrel, Thibault, Hensel, Felix, Carrière, Mathieu, Lacombe, Théo, Ike, Yuichi, Kurihara, Hiroaki, Glisse, Marc, Chazal, Frédéric
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
Externí odkaz:
http://arxiv.org/abs/2202.01725
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular pieces-ca
Externí odkaz:
http://arxiv.org/abs/2109.00530