Computational Topology

Edelsbrunner, H., & Harer, J. (2010). Computational Topology: An Introduction.

Type

Book

Intellectual base

Review or monograph

Year

2010

Link

https://bookstore.ams.org/mbk-69

Cited from

mathematics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Modifiable Areal Unit Problem
  • Quotient structures in algebra make a quotient's properties depend on the equivalence relation chosen. Resolution-dependent objects like persistent homology have features that exist at one scale and not another.
• Topology
  • … development in which topological methods (most prominently persistent homology, but also the mapper algorithm and various topological feature-extraction techniques) are applied to high-dimensional point-cloud data to extract robust qualitative-structural features that are stable under small perturbations of the data.

    This sourceThe standard textbook on computational and applied topology, including persistent homology and the algorithmic foundations of topological data analysis.

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