2015/12/01 by Michael Lesnick, Matthew Wright, Lesnick, Michael +1 · 5 citations
Computer Science · Medicine · #Advanced Neuroimaging Techniques and Applications #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #Computational Geometry (cs.CG) #Data Visualization and Analytics #FOS: Computer and information sciences #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1512.00180
openalex publication_date 2015/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.