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Vietoris–Rips complex

Known as: Rips complex, Vietoris complex, Vietoris-Rips complex 
In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is an abstract simplicial complex that can be defined from… 
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Related topics

Related topics

7 relations
Clique (graph theory)Computer scienceGeodesic convexityTopological data analysis

Broader (1)

Geometric graph theory

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2018
2018
Bestvina–Brady discrete Morse theory and Vietoris–Rips complexes
abstract:We inspect Vietoris--Rips complexes ${\cal{VR}}_t(X)$ of certain metric spaces $X$ using a new generalization of… 
2018
2018
Vietoris-Rips Complexes of Regular Polygons.
Persistent homology has emerged as a novel tool for data analysis in the past two decades. However, there are still very few… 
2018
2018
On the choice of weight functions for linear representations of persistence diagrams
Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert… 
2017
2017
Persistent entropy for separating topological features from noise in vietoris-rips complexes
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a… 
2015
2015
Random cyclic dynamical systems
Review
2014
Review
2014
Introduction to the R package TDA
We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis… 
2014
2014
Numeric invariants from multidimensional persistence
Topological data analysis is the study of data using techniques from algebraic topology. Often, one begins with a finite set of… 
Highly Cited
2012
Highly Cited
2012
Linear-Size Approximations to the Vietoris–Rips Filtration
The Vietoris–Rips filtration is a versatile tool in topological data analysis. It is a sequence of simplicial complexes built on… 
Highly Cited
2009
Highly Cited
2009
Vietoris–Rips Complexes of Planar Point Sets
AbstractFix a finite set of points in Euclidean n-space $\mathbb{E}^{n}$ , thought of as a point-cloud sampling of a certain… 
Highly Cited
2009
Highly Cited
2009
Random Geometric Complexes
We study the expected topological properties of Čech and Vietoris–Rips complexes built on random points in ℝd. We find higher… 
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