Challenges in topological object data analysis

DOI10.1007/s13171-018-0137-7zbMath1422.62234arXiv1804.10255OpenAlexW3105581800WikidataQ125974788 ScholiaQ125974788MaRDI QIDQ2317002

Robert Paige, Daniel E. Osborne, Peter Bubenik, Victor Patrangenaru

Publication date: 7 August 2019

Published in: Sankhyā. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10255

zbMATH Keywords

topological data analysisrelative homologypersistence landscapesobject data analysisVeronese-Whitney (VW) embeddingVW-means of index \(r\)

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Image analysis in multivariate analysis (62H35) Singularities of differentiable mappings in differential topology (57R45) ?ech types (55N05) Connections of general topology with other structures, applications (54H99)

Related Items

Test for homogeneity of random objects on manifolds with applications to biological shape analysis ⋮ Bayesian topological learning for classifying the structure of biological networks ⋮ Topological learning for brain networks ⋮ The Persistence Landscape and Some of Its Properties ⋮ Topological Object Data Analysis Methods with an Application to Medical Imaging ⋮ Extrinsic regression and anti-regression on projective shape manifolds ⋮ Persistent homology detects curvature ⋮ A random persistence diagram generator ⋮ A Bayesian Framework for Persistent Homology

Uses Software

• TDA
• Persistence Landscape
• GitHub
• Ripser

Cites Work

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