Euler characteristic tools for topological data analysis
O Hacquard, V Lebovici - Journal of Machine Learning Research, 2024 - jmlr.org
In this article, we study Euler characteristic techniques in topological data analysis.
Pointwise computing the Euler characteristic of a family of simplicial complexes built from …
Pointwise computing the Euler characteristic of a family of simplicial complexes built from …
Graphcode: Learning from multiparameter persistent homology using graph neural networks
We introduce graphcodes, a novel multi-scale summary of the topological properties of a
dataset that is based on the well-established theory of persistent homology. Graphcodes …
dataset that is based on the well-established theory of persistent homology. Graphcodes …
Topology-driven goodness-of-fit tests in arbitrary dimensions
P Dłotko, N Hellmer, Ł Stettner, R Topolnicki - Statistics and Computing, 2024 - Springer
This paper adopts a tool from computational topology, the Euler characteristic curve (ECC)
of a sample, to perform one-and two-sample goodness of fit tests. We call our procedure …
of a sample, to perform one-and two-sample goodness of fit tests. We call our procedure …
Stability for Inference with Persistent Homology Rank Functions
Q Wang, I García‐Redondo, P Faugère… - Computer Graphics …, 2024 - Wiley Online Library
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis
that capture the “shape” of a wide range of complex data structures, such as point clouds …
that capture the “shape” of a wide range of complex data structures, such as point clouds …
Topological Dynamics of Functional Neural Network Graphs During Reinforcement Learning
This study investigates the topological structures of neural network activation graphs, with a
focus on detecting higher-order Betti numbers during reinforcement learning. The paper …
focus on detecting higher-order Betti numbers during reinforcement learning. The paper …
Graphcode: Learning from multiparameter persistent homology using graph neural networks
We introduce graphcodes, a novel multi-scale summary of the topological properties of a
dataset that is based on the well-established theory of persistent homology. Graphcodes …
dataset that is based on the well-established theory of persistent homology. Graphcodes …
Probabilistic Analysis of Multiparameter Persistence Decompositions into Intervals
Multiparameter persistence modules can be uniquely decomposed into indecomposable
summands. Among these indecomposables, intervals stand out for their simplicity, making …
summands. Among these indecomposables, intervals stand out for their simplicity, making …
Probabilistic Analysis of Multiparameter Persistence Decompositions
Multiparameter persistence modules can be uniquely decomposed into indecomposable
summands. Among these indecomposables, intervals stand out for their simplicity, making …
summands. Among these indecomposables, intervals stand out for their simplicity, making …
Advances in random topology
O Bobrowski, D Yogeshwaran - Journal of Applied and Computational …, 2024 - Springer
Random topology refers to the study of topological properties of randomly generated
spaces. This area of research dates back to the seminal result by Erdos and Rényi on the …
spaces. This area of research dates back to the seminal result by Erdos and Rényi on the …
Wasserstein convergence of Čech persistence diagrams for samplings of submanifolds
\v Cech Persistence diagrams (PDs) are topological descriptors routinely used to capture the
geometry of complex datasets. They are commonly compared using the Wasserstein …
geometry of complex datasets. They are commonly compared using the Wasserstein …