95 citations · 620 across the 56 of their papers we have counts for
6 papers · 1 filter
On Homotopy Types of Vietoris-Rips Complexes of Metric Gluings
Michal Adamaszek, Henry Adams, Ellen Gasparovic +6
We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equival…
Unperturbed: spectral analysis beyond Davis-Kahan
Justin Eldridge, Mikhail Belkin, Yusu Wang
Classical matrix perturbation results, such as Weyl's theorem for eigenvalues and the Davis-Kahan theorem for eigenvectors, are general purpose. These classical bounds are tight in…
Topological Analysis of Nerves, Reeb Spaces, Mappers, and Multiscale Mappers
Tamal K. Dey, Facundo Memoli, Yusu Wang
Data analysis often concerns not only the space where data come from, but also various types of maps attached to data. In recent years, several related structures have been used to…
A quest to unravel the metric structure behind perturbed networks
Srinivasan Parthasarathy, David Sivakoff, Minghao Tian +1
Graphs and network data are ubiquitous across a wide spectrum of scientific and application domains. Often in practice, an input graph can be considered as an observed snapshot of…
Analyzing and Visualizing Scalar Fields on Graphs
Yang Zhang, Yusu Wang, Srinivasan Parthasarathy
The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. E…
A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road…