41 citations · 264 across the 40 of their papers we have counts for
8 papers · 1 filter
New families of simplicial filtration functors
Samir Chowdhury, Nathaniel Clause, Facundo Memoli +2
The so called Čech and Vietoris-Rips simplicial filtrations are designed to capture information about the topological structure of metric datasets. These filtrations are two of the…
Convergence of Hierarchical Clustering and Persistent Homology Methods on Directed Networks
Samir Chowdhury, Facundo Mémoli
While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known ab…
The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data
Samir Chowdhury, Bowen Dai, Facundo Mémoli
We develop of a line of work initiated by Curto and Itskov towards understanding the amount of information contained in the spike trains of hippocampal place cells via topology con…
Distances and Isomorphism between Networks: Stability and Convergence of Network Invariants
Samir Chowdhury, Facundo Mémoli
We develop the theoretical foundations of a generalized Gromov-Hausdorff distance between functions on networks that has recently been applied to various subfields of topological d…
A Distance Between Filtered Spaces Via Tripods
Facundo Memoli
We present a simplified treatment of stability of filtrations on finite spaces. Interestingly, we can lift the stability result for combinatorial filtrations from [CSEM06] to the c…
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…