# cech complex

Published articles for cech complex.

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## The Čech Complex and the Vietoris-Rips Complex

DevFeed: [The Čech Complex and the Vietoris-Rips Complex](<https://devfeed.tech/articles/the-cech-complex-and-the-vietoris-rips-complex-40386.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/08/06/cech-vietoris-rips-complex/>)

Published: 2015-08-06T09:00:00Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [data](<https://devfeed.tech/topics/data.md>), [datasets](<https://devfeed.tech/topics/datasets.md>), [Point cloud](<https://devfeed.tech/topics/point-cloud.md>), [Computing](<https://devfeed.tech/topics/computing.md>)

Tags: [approximation](<https://devfeed.tech/tags/approximation.md>), [cech-complex](<https://devfeed.tech/tags/cech-complex.md>), [complex](<https://devfeed.tech/tags/complex.md>), [computational-topology](<https://devfeed.tech/tags/computational-topology.md>), [data-mining](<https://devfeed.tech/tags/data-mining.md>), [data-science](<https://devfeed.tech/tags/data-science.md>), [dataset](<https://devfeed.tech/tags/dataset.md>), [homology](<https://devfeed.tech/tags/homology.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [persistent-homology](<https://devfeed.tech/tags/persistent-homology.md>), [point](<https://devfeed.tech/tags/point.md>), [points](<https://devfeed.tech/tags/points.md>), [simplicial-complex](<https://devfeed.tech/tags/simplicial-complex.md>), [vietoris-rips-complex](<https://devfeed.tech/tags/vietoris-rips-complex.md>)

### AI overview

This article introduces computational topology for analyzing the shape of data. It explains how point clouds can be converted into simplicial complexes so homology and persistent homology can identify qualitative features such as connected components and holes, with some resistance to noise.

### Source excerpt

It's about time we got back to computational topology. Previously in this series we endured a lightning tour of the fundamental group and homology, then we saw how to compute the homology of a simplicial complex using linear algebra. What we really want to do is talk about the inherent shape of data. Homology allows us to compute some qualitative features of a given shape, i.e., find and count the number of connected components or a given shape, or the number of "2-dimensional holes" it has.