56 citations · 106 across the 17 of their papers we have counts for
4 papers · 1 filter
Cross-Matched Interval Prevalence of High Dimensional Point Clouds
Jonathan M. Mousley, Paul Bendich
Topological Data Analysis (TDA) has been applied with success to solve problems across many scientific disciplines. However, in the setting of a point cloud sampled from a shap…
Convolutional Persistence Transforms
Elchanan Solomon, Paul Bendich
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filte…
From Geometry to Topology: Inverse Theorems for Distributed Persistence
Elchanan Solomon, Alexander Wagner, Paul Bendich
What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to…
Persistent Obstruction Theory for a Model Category of Measures with Applications to Data Merging
Abraham D. Smith, Paul Bendich, John Harer
Collections of measures on compact metric spaces form a model category ("data complexes"), whose morphisms are marginalization integrals. The fibrant objects in this category repre…