56 citations · 106 across the 17 of their papers we have counts for
4 papers · 1 filter
Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology
Paul Bendich, Ellen Gasparovic, Christopher J. Tralie +1
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produce…
Stabilizing the unstable output of persistent homology computations
Paul Bendich, Peter Bubenik, Alexander Wagner
We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is…
Multi-Scale Local Shape Analysis and Feature Selection in Machine Learning Applications
Paul Bendich, Ellen Gasparovic, John Harer +2
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both g…
Homology and Robustness of Level and Interlevel Sets
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov +1
Given a function $f: \Xspace \to \Rspace$ on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups fr…