Table of Contents
11 relations: Alpha shape, Chain complex, Geometric and Topological Inference, Homological connectivity, Leray spectral sequence, List of eponyms (A–K), Offset filtration, Persistent homology, Topological data analysis, Vietoris–Rips complex, Vietoris–Rips filtration.
Alpha shape
In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points.
See Čech complex and Alpha shape
Chain complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.
See Čech complex and Chain complex
Geometric and Topological Inference
Geometric and Topological Inference is a monograph in computational geometry, computational topology, geometry processing, and topological data analysis, on the problem of inferring properties of an unknown space from a finite point cloud of noisy samples from the space.
See Čech complex and Geometric and Topological Inference
Homological connectivity
In algebraic topology, homological connectivity is a property describing a topological space based on its homology groups.
See Čech complex and Homological connectivity
Leray spectral sequence
In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray.
See Čech complex and Leray spectral sequence
List of eponyms (A–K)
An eponym is a person (real or fictitious) from whom something is said to take its name.
See Čech complex and List of eponyms (A–K)
Offset filtration
The offset filtration (also called the "union-of-balls" or "union-of-disks" filtration) is a growing sequence of metric balls used to detect the size and scale of topological features of a data set.
See Čech complex and Offset filtration
Persistent homology
Persistent homology is a method for computing topological features of a space at different spatial resolutions.
See Čech complex and Persistent homology
Topological data analysis
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology.
See Čech complex and Topological data analysis
Vietoris–Rips complex
In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is a way of forming a topological space from distances in a set of points.
See Čech complex and Vietoris–Rips complex
Vietoris–Rips filtration
In topological data analysis, the Vietoris–Rips filtration (sometimes shortened to "Rips filtration") is the collection of nested Vietoris–Rips complexes on a metric space created by taking the sequence of Vietoris–Rips complexes over an increasing scale parameter.
See Čech complex and Vietoris–Rips filtration
References
Also known as Cech complex.