Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

DOI10.1016/j.physd.2016.03.007zbMath1415.60052arXiv1507.01454OpenAlexW801015201WikidataQ62387250 ScholiaQ62387250MaRDI QIDQ1999944

Vanessa Robins, Katharine Turner

Publication date: 27 June 2019

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01454

zbMATH Keywords

stochastic geometryBetti numberstopological data analysis

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Other homology theories in algebraic topology (55N35)

Related Items (16)

Persistence diagrams with linear machine learning models ⋮ Signal classification with a point process distance on the space of persistence diagrams ⋮ Aspects of topological approaches for data science ⋮ Distributing persistent homology via spectral sequences ⋮ Topological learning for brain networks ⋮ The Persistence Landscape and Some of Its Properties ⋮ Same But Different: Distance Correlations Between Topological Summaries ⋮ Geometric Metrics for Topological Representations ⋮ Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases ⋮ Kernel method for persistence diagrams via kernel embedding and weight factor ⋮ Editorial: Topology in dynamics, differential equations, and data ⋮ On the expectation of a persistence diagram by the persistence weighted kernel ⋮ Hypothesis testing for topological data analysis ⋮ Unnamed Item ⋮ Persistent homology detects curvature ⋮ The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications

Uses Software

• spatstat
• javaPlex
• PHAT
• kepler98

Cites Work

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• Betti numbers in multidimensional persistent homology are stable functions
• javaPlex: A Research Software Package for Persistent (Co)Homology
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• Statistical topology via Morse theory, persistence and nonparametric estimation
• Topology and data
• Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings
• Three-dimensional alpha shapes
• Morphological Characterization of Point Patterns
• Zigzag persistent homology and real-valued functions
• PERSISTENCE BARCODES FOR SHAPES
• Statistical topological data analysis using persistence landscapes

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