Interactive Visualization of 2-D Persistence Modules

Abstract

The goal of this work is to extend the standard persistent homology pipeline for exploratory data analysis to the 2-D persistence setting, in a practical, computationally efficient way. To this end, we introduce RIVET, a software tool for the visualization of 2-D persistence modules, and present mathematical foundations for this tool. RIVET provides an interactive visualization of the barcodes of 1-D affine slices of a 2-D persistence module M . It also computes and visualizes the dimension of each vector space in M and the bigraded Betti numbers of M . At the heart of our computational approach is a novel data structure based on planar line arrangements, on which we can perform fast queries to find the barcode of any slice of M . We present an efficient algorithm for constructing this data structure and establish bounds on its complexity.

Extracted Key Phrases

18 Figures and Tables

Cite this paper

@article{Lesnick2015InteractiveVO, title={Interactive Visualization of 2-D Persistence Modules}, author={Michael Lesnick and Matthew J Wright}, journal={CoRR}, year={2015}, volume={abs/1512.00180} }