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Topological Data Analysis

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Cover of 'Topological Data Analysis'

Table of Contents

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    Book Overview
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    Chapter 1 A Fractal Dimension for Measures via Persistent Homology
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    Chapter 2 DTM-Based Filtrations
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    Chapter 3 Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem
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    Chapter 4 The Persistence Landscape and Some of Its Properties
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    Chapter 5 Topological Approaches to Deep Learning
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    Chapter 6 Topological Data Analysis of Single-Cell Hi-C Contact Maps
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    Chapter 7 Neural Ring Homomorphisms and Maps Between Neural Codes
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    Chapter 8 Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally
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    Chapter 9 Iterated Integrals and Population Time Series Analysis
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    Chapter 10 Prediction in Cancer Genomics Using Topological Signatures and Machine Learning
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    Chapter 11 Topological Adventures in Neuroscience
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    Chapter 12 Percolation on Homology Generators in Codimension One
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    Chapter 13 Hyperplane Neural Codes and the Polar Complex
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    Chapter 14 Analysis of Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence
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    Chapter 15 Canonical Stratifications Along Bisheaves
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    Chapter 16 Inverse Problems in Topological Persistence
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    Chapter 17 Sparse Circular Coordinates via Principal ℤ $$\mathbb {Z}$$ -Bundles
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    Chapter 18 Same But Different: Distance Correlations Between Topological Summaries
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    Chapter 19 Certified Mapper: Repeated Testing for Acyclicity and Obstructions to the Nerve Lemma
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Title
Topological Data Analysis
Published by
Springer International Publishing, June 2020
DOI 10.1007/978-3-030-43408-3
ISBNs
978-3-03-043407-6, 978-3-03-043408-3
Editors

Baas, Nils A., Carlsson, Gunnar E., Quick, Gereon, Szymik, Markus, Thaule, Marius

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