20 citations · 31 across the 10 of their papers we have counts for
13 papers
Observable Covariance and Principal Observable Analysis for Data on Metric Spaces
Ece Karacam, Washington Mio, Osman Berat Okutan
Datasets consisting of objects such as shapes, networks, images, or signals overlaid on such geometric objects permeate data science. Such datasets are often equipped with metrics…
Stability and Approximations for Decorated Reeb Spaces
Justin Curry, Washington Mio, Tom Needham +2
Given a map from a topological space to a metric space , a decorated Reeb space consists of the Reeb space, together with an attribution function whose values re…
On Metrics for Analysis of Functional Data on Geometric Domains
Soheil Anbouhi, Washington Mio, Osman Berat Okutan
This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces,…
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…
Universal Mappings and Analysis of Functional Data on Geometric Domains
Soheil Anbouhi, Washington Mio, Osman Berat Okutan
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Data…
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…
Metric Graph Approximations of Geodesic Spaces
Facundo Memoli, Osman Berat Okutan, Qingsong Wang
We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitabl…
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…
The Distortion of the Reeb Quotient Map on Riemannian Manifolds
Facundo Mémoli, Osman Berat Okutan
Given a metric space and a function , the Reeb construction gives metric a space together with a quotient map . Under suitable conditions…
Reeb Posets and Tree Approximations
Facundo Mémoli, Osman Berat Okutan
A well known result in the analysis of finite metric spaces due to Gromov says that given any there exists a \emph{tree metric} on such that $\|d_X-t_X\|_\infty…
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…