56 citations · 106 across the 17 of their papers we have counts for
22 papers
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…
Topological Parallax: A Geometric Specification for Deep Perception Models
Abraham D. Smith, Michael J. Catanzaro, Gabrielle Angeloro +2
For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine…
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…
Topological Simplification of Signals for Inference and Approximate Reconstruction
Gary Koplik, Nathan Borggren, Sam Voisin +4
As Internet of Things (IoT) devices become both cheaper and more powerful, researchers are increasingly finding solutions to their scientific curiosities both financially and compu…
Improving Metric Dimensionality Reduction with Distributed Topology
Alexander Wagner, Elchanan Solomon, Paul Bendich
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method…
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…