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Čech complex

In algebraic topology and topological data analysis, the Čech complex is an abstract simplicial complex constructed from a point cloud in any metric space which is meant to capture topological information about the point cloud or the distribution it is drawn from. Given a finite point cloud X and an ε > 0, we construct the Čech complex C ˇ ε ( X )…

Relation to Vietoris–Rips complex & Overview

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Relation to Vietoris–Rips complex

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Čech complex

Nodes13
Edges12
Triples8
Avg. degree1.85
Density0.153846
Components1

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Čech complex

Top relations

related to Relation to Vietoris–Rips complex · 5
Čech complex → Rips, The, The Vietoris, Vietoris, While
is a · 3
Čech complex → abstract simplicial complex constructed from a point cloud in any metric space which is meant to capture topological information about the point cloud or the distribution it is…, nerve of the set of ε-balls centered at points of X, subcomplex of the Vietoris

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Important terminology

complex čech set nerve check vietoris rips point cloud displaystyle varepsilon ε-balls centered points also simplicial homotopy equivalent union balls

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Čech complexis aabstract simplicial complex constructed from a point cloud in any metric space which is meant to capture topological information about the point cloud or the distribution it is…0.90text
Čech complexis anerve of the set of ε-balls centered at points of X0.90text
Čech complexis asubcomplex of the Vietoris0.90text
Čech complexrelated to Relation to Vietoris–Rips complexThe0.60section
Čech complexrelated to Relation to Vietoris–Rips complexVietoris0.60section
Čech complexrelated to Relation to Vietoris–Rips complexRips0.60section
Čech complexrelated to Relation to Vietoris–Rips complexWhile0.60section
Čech complexrelated to Relation to Vietoris–Rips complexThe Vietoris0.60section

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    Min side: 3
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