41 citations · 264 across the 40 of their papers we have counts for
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Sketching and Clustering Metric Measure Spaces
Facundo Mémoli, Anastasios Sidiropoulos, Kritika Singhal
Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric me…
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…
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…
The Persistent Homotopy Type Distance
Patrizio Frosini, Claudia Landi, Facundo Memoli
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in…
Mutiscale Mapper: A Framework for Topological Summarization of Data and Maps
Tamal K. Dey, Facundo Memoli, Yusu Wang
Summarizing topological information from datasets and maps defined on them is a central theme in topological data analysis. \textsf{Mapper}, a tool for such summarization, takes as…