Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide

no code implementations • 14 May 2021 • Lu Li, Connor Thompson, Gregory Henselman-Petrusek, Chad Giusti, Lori Ziegelmeier

Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data.

Capturing Dynamics of Time-Varying Data via Topology

no code implementations • 7 Oct 2020 • Lu Xian, Henry Adams, Chad M. Topaz, Lori Ziegelmeier

One approach to understanding complex data is to study its shape through the lens of algebraic topology.

Topological Data Analysis

Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies

no code implementations • 7 Jul 2016 • Sofya Chepushtanova, Michael Kirby, Chris Peterson, Lori Ziegelmeier

This realization has motivated the development of new tools such as persistent homology for exploring topological invariants, or features, in large data sets.

Topological Data Analysis

Persistence Images: A Stable Vector Representation of Persistent Homology

4 code implementations • 22 Jul 2015 • Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta, Rachel Neville, Chris Peterson, Patrick Shipman, Lori Ziegelmeier

We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs.

BIG-bench Machine Learning Graph Classification +1