Proximity of persistence modules and their diagrams
From MaRDI portal
Publication:5370722
DOI10.1145/1542362.1542407zbMath1380.68387OpenAlexW2056761334WikidataQ59442771 ScholiaQ59442771MaRDI QIDQ5370722
David Cohen-Steiner, Marc Glisse, Steve Y. Oudot, Fréderic Chazal, Leonidas J. Guibas
Publication date: 20 October 2017
Published in: Proceedings of the twenty-fifth annual symposium on Computational geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1145/1542362.1542407
Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35)
Related Items
Geometric and probabilistic limit theorems in topological data analysis, Generalized persistence diagrams, Structure and stability of the one-dimensional Mapper, Higher Interpolation and Extension for Persistence Modules, Topological graph persistence, Hausdorff stability of persistence spaces, Rank-based persistence, Signal classification with a point process distance on the space of persistence diagrams, Algebraic stability of zigzag persistence modules, Persistent Homology: A Topological Tool for Higher-Interaction Systems, Categorified Reeb graphs, Universality of persistence diagrams and the bottleneck and Wasserstein distances, Aspects of topological approaches for data science, A topological approach for protein classification, Piecewise Linear Sheaves, Efficient and robust persistent homology for measures, Linear-size approximations to the Vietoris-Rips filtration, Metric Reconstruction Via Optimal Transport, On \(p\)-metric spaces and the \(p\)-Gromov-Hausdorff distance, On the Hofer-Zehnder conjecture, Viterbo conjecture for Zoll symmetric spaces, Ephemeral persistence modules and distance comparison, \(A_\infty\) persistent homology estimates detailed topology from pointcloud datasets, The persistent homology of a self-map, Asymptotic theory for density ridges, Finiteness of rank invariants of multidimensional persistent homology groups, Field choice problem in persistent homology, Interleavings and matchings as representations, Universality of the homotopy interleaving distance, Connectedness and Lusternik-Schnirelmann categories of the spaces of persistence modules, Metrics for generalized persistence modules, Multidimensional persistence and noise, Stabilizing the unstable output of persistent homology computations, The Morse theory of Čech and Delaunay complexes, Bottleneck stability for generalized persistence diagrams, Stable comparison of multidimensional persistent homology groups with torsion, Filtration simplification for persistent homology via edge contraction, Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem, The Persistence Landscape and Some of Its Properties, Analysis of Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence, Inverse Problems in Topological Persistence, Embeddings of persistence diagrams into Hilbert spaces, Moduli spaces of Morse functions for persistence, Zigzag persistence, Scalar field analysis over point cloud data, Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis, Persistence stability for geometric complexes, Persistent homology and the upper box dimension, Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018, Rigorous cubical approximation and persistent homology of continuous functions, Measuring the Error in Approximating the Sub-Level Set Topology of Sampled Scalar Data, Spatiotemporal persistent homology for dynamic metric spaces, Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability, Polynomial-sized topological approximations using the permutahedron, Improved approximate Rips filtrations with shifted integer lattices and cubical complexes, The persistent homology of a sampled map: from a viewpoint of quiver representations, Categorification of persistent homology, Robust Topological Inference: Distance To a Measure and Kernel Distance, Comparison of persistent homologies for vector functions: from continuous to discrete and back, Parametrized homology via zigzag persistence, Theory of interleavings on categories with a flow, Persistent intersection homology, Improved Approximate Rips Filtrations with Shifted Integer Lattices, Computational Complexity of the Interleaving Distance, Rips filtrations for quasimetric spaces and asymmetric functions with stability results, An approximate nerve theorem, Persistence modules on commutative ladders of finite type, On the stability of interval decomposable persistence modules, Quantifying Genetic Innovation: Mathematical Foundations for the Topological Study of Reticulate Evolution, Reconstruction of compacta by finite approximations and inverse persistence, Persistent homology for hypergraphs and computational tools — A survey for users, Unnamed Item, Persistent homology of the sum metric, A topological study of functional data and Fréchet functions of metric measure spaces, Barcodes and area-preserving homeomorphisms, Generalized persistence diagrams for persistence modules over posets, A derived isometry theorem for sheaves, A brief introduction to multidimensional persistent Betti numbers, Persistent homology and microlocal sheaf theory, A functorial Dowker theorem and persistent homology of asymmetric networks, Topological spaces of persistence modules and their properties, Sparse Dowker nerves, A comparison framework for interleaved persistence modules, The reflection distance between zigzag persistence modules, Decorated merge trees for persistent topology, Fractal dimension and the persistent homology of random geometric complexes, G -invariant persistent homology, Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics, SimBa, Betti numbers in multidimensional persistent homology are stable functions, Unnamed Item, Probabilistic Fréchet means for time varying persistence diagrams, Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology, A topological measurement of protein compressibility, Approximating persistent homology in Euclidean space through collapses, The theory of the interleaving distance on multidimensional persistence modules, Sliding windows and persistence: an application of topological methods to signal analysis, Combining persistent homology and invariance groups for shape comparison, Relative interleavings and applications to sensor networks, Stable volumes for persistent homology, A directed persistent homology theory for dissimilarity functions, Thickening of the diagonal and interleaving distance, Steady and ranging sets in graph persistence, The (homological) persistence of gerrymandering, Rectification of interleavings and a persistent Whitehead theorem, Time-Inhomogeneous Diffusion Geometry and Topology, Exact weights, path metrics, and algebraic Wasserstein distances, Distances and isomorphism between networks: stability and convergence of network invariants, Persistence and the Sheaf-Function Correspondence, Unnamed Item