A statistical approach to persistent homology
From MaRDI portal
Publication:2457230
DOI10.4310/HHA.2007.v9.n2.a12zbMath1136.55004arXivmath/0607634MaRDI QIDQ2457230
Publication date: 30 October 2007
Published in: Homology, Homotopy and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0607634
directional statisticspersistent homologypoint cloud dataparametric statisticsexpected persistent homology
Directional data; spatial statistics (62H11) Homology and cohomology theories in algebraic topology (55N99)
Related Items
Geometric and probabilistic limit theorems in topological data analysis, Topology of random geometric complexes: a survey, EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY, Object-oriented persistent homology, Aspects of topological approaches for data science, Path homology theory of edge-colored graphs, Bootstrapping persistent Betti numbers and other stabilizing statistics, Random geometric complexes, The Persistence Landscape and Some of Its Properties, Multiscale persistent functions for biomolecular structure characterization, Topological Object Data Analysis Methods with an Application to Medical Imaging, Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport, Persistence barcodes versus Kolmogorov signatures: detecting modes of one-dimensional signals, Topological Analysis of Variance and the Maxillary Complex, Confidence sets for persistence diagrams, Hypothesis testing for topological data analysis, Exploring uses of persistent homology for statistical analysis of landmark-based shape data, The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation, Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications, Computational tools in weighted persistent homology, Persistent homology detects curvature, HERMES: persistent spectral graph software, Barcodes: The persistent topology of data, Biomolecular topology: modelling and analysis, The topology of probability distributions on manifolds, Topological data analysis for the energy and stability of endohedral metallofullerenes
