20 citations · 31 across the 10 of their papers we have counts for
6 papers · 1 filter
Topologically Attributed Graphs for Shape Discrimination
Justin Curry, Washington Mio, Tom Needham +2
In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction,…
Convergence of Leray Cosheaves for Decorated Mapper Graphs
Justin Curry, Washington Mio, Tom Needham +2
We introduce decorated mapper graphs as a generalization of mapper graphs capable of capturing more topological information of a data set. A decorated mapper graph can be viewed as…
Decorated Merge Trees for Persistent Topology
Justin Curry, Haibin Hang, Washington Mio +2
This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both and information into a single data structure that disti…
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Sunhyuk Lim, Facundo Memoli, Osman Berat Okutan
In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information f…
Quantitative Simplification of Filtered Simplicial Complexes
Facundo Mémoli, Osman Berat Okutan
We introduce a new invariant defined on the vertices of a given filtered simplicial complex, called codensity, which controls the impact of removing vertices on persistent homology…
Free Actions on Products of Spheres at High Dimensions
Osman Berat Okutan, Ergun Yalcin
A classical conjecture in transformation group theory states that if acts freely on a product of spheres , then . We…