9 citations · 10 across the 3 of their papers we have counts for
5 papers
A Lattice-Theoretic Perspective on the Persistence Map
Brendan Mallery, Adélie Garin, Justin Curry
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our d…
From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem
Justin Curry, Jordan DeSha, Adélie Garin +3
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered con…
From trees to barcodes and back again: theoretical and statistical perspectives
Lida Kanari, Adélie Garin, Kathryn Hess
Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topologi…
Duality in Persistent Homology of Images
Adélie Garin, Teresa Heiss, Kelly Maggs +2
We derive the relationship between the persistent homology barcodes of two dual filtered CW complexes. Applied to greyscale digital images, we obtain an algorithm to convert barcod…
A Topological "Reading" Lesson: Classification of MNIST using TDA
Adélie Garin, Guillaume Tauzin
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological feature…