# persistent homology

Published articles for persistent homology.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## 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.

## Fixing Bugs in "Computing Homology"

DevFeed: [Fixing Bugs in "Computing Homology"](<https://devfeed.tech/articles/fixing-bugs-in-computing-homology-40340.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/01/23/fixing-bugs-in-computing-homology/>)

Published: 2014-01-23T23:05:16Z

Content type: tutorial

Language: en

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

Topics: [Computing](<https://devfeed.tech/topics/computing.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Code](<https://devfeed.tech/topics/code.md>), [function](<https://devfeed.tech/topics/function.md>), [Matrix](<https://devfeed.tech/topics/matrix-org.md>)

Tags: [bugs](<https://devfeed.tech/tags/bugs.md>), [code](<https://devfeed.tech/tags/code.md>), [computing](<https://devfeed.tech/tags/computing.md>), [function](<https://devfeed.tech/tags/function.md>), [homology](<https://devfeed.tech/tags/homology.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [persistent-homology](<https://devfeed.tech/tags/persistent-homology.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [quotients](<https://devfeed.tech/tags/quotients.md>), [row-reduction](<https://devfeed.tech/tags/row-reduction.md>), [test](<https://devfeed.tech/tags/test.md>)

### AI overview

This article corrects bugs in code for computing homology. It identifies an indexing error, explains a mathematical mistake in simultaneous row and column reduction, and shows how further row reduction is needed to obtain the correct rank for a triangulation of the Möbius band.

### Source excerpt

A few awesome readers have posted comments in Computing Homology to the effect of, "Your code is not quite correct!" And they're right! Despite the almost year since that post's publication, I haven't bothered to test it for more complicated simplicial complexes, or even the basic edge cases! When I posted it the mathematics just felt so solid to me that it had to be right (the irony is rich, I know).