Fix the definition of the Vietoris-Rips Complex - #39
Open
haiderriazkhan wants to merge 1 commit into
Open
Conversation
The previous wording incorrectly suggested that the 0- and 1-simplices themselves constitute a Vietoris–Rips complex. A Vietoris–Rips complex can contain higher-dimensional simplices, but it is completely determined by its 1-skeleton: whenever a set of vertices is pairwise connected, the corresponding higher-dimensional simplex is included. This change also clarifies the preceding Čech construction by describing simplices as arising from sets of points whose neighborhoods have a non-empty common intersection, not "points that overlap." For reference, see: [1]. https://www.youtube.com/watch?v=pn123oUaiDk&t=282s [2]. https://arxiv.org/pdf/1710.04019
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
The previous wording incorrectly suggested that the 0- and 1-simplices themselves constitute a Vietoris–Rips Complex. A Vietoris–Rips Complex can contain higher-dimensional simplices, but it is completely determined by its 1-skeleton: whenever a set of vertices is pairwise connected, the corresponding higher dimensional simplex is included.
This change also clarifies the preceding Čech construction by describing simplices as arising from sets of points whose neighborhoods have a non-empty common intersection.
For reference, see:
[1]. https://www.youtube.com/watch?v=pn123oUaiDk&t=282s
[2]. https://arxiv.org/pdf/1710.04019