16 citations · 41 across the 5 of their papers we have counts for
7 papers
A Categorical Approach to Möbius Inversion via Derived Functors
Alex Elchesen, Amit Patel
We develop a cohomological approach to Möbius inversion using derived functors in the enriched categorical setting. For a poset and a closed symmetric monoidal abelian category…
Relative Optimal Transport
Peter Bubenik, Alex Elchesen
We develop a theory of optimal transport relative to a distinguished subset, which acts as a reservoir of mass, allowing us to compare measures of different total variation. This r…
Learning on Persistence Diagrams as Radon Measures
Alex Elchesen, Iryna Hartsock, Jose A. Perea +1
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures…
Topological data analysis of C. elegans locomotion and behavior
Ashleigh Thomas, Kathleen Bates, Alex Elchesen +3
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of co…
Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces
Peter Bubenik, Alex Elchesen
Persistence diagrams, an important summary in topological data analysis, consist of a set of ordered pairs, each with positive multiplicity. Persistence diagrams are obtained via M…
Universality of persistence diagrams and the bottleneck and Wasserstein distances
Peter Bubenik, Alex Elchesen
We prove that persistence diagrams with the p-Wasserstein distance form the universal p-subadditive commutative monoid on an underlying metric space with a distinguished subset. Th…
The reflection distance between zigzag persistence modules
Alexander Elchesen, Facundo Mémoli
By invoking the reflection functors introduced by Bernstein, Gelfand, and Ponomarev in 1973, in this paper we define a metric on the space of all zigzag modules of a given length,…