Online Program Home
  My Program

Abstract Details

Activity Number: 293 - SPEED: Computing, Graphics, and Programming Statistics
Type: Contributed
Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Graphics
Abstract #322650 View Presentation
Title: Persistence Terrace for Topological Inference of Point Cloud Data
Author(s): Chul Moon* and Noah Giansiracusa and Nicole Lazar
Companies: University of Georgia and Swarthmore College and University of Georgia
Keywords: topological data analysis ; persistent homology ; density estimation ; visualization

We propose a new plot, called the persistence terrace, that reveals the topological features of point cloud data. The topological characteristics of a topological space can be estimated robustly to noise and outliers by smoothing; construct a manifold with the point cloud using a smoothing function and compute persistent homology of the level set of the smoothed manifold. We construct manifolds with several smoothing parameters and apply persistent homology. The persistence terrace visualizes the computed persistent homology results of the manifolds. In the k-dimensional persistence terrace, we plot the kth Betti number against the filtration value and smoothing parameter. A k-dimensional hole is represented as a discrete staircase region; overlapping regions stack. The persistence terrace allows for the investigation of the topological characteristics of the space without the need to choose the optimal smoothing parameter. Furthermore, we can infer size and point density of a topological feature by examining the length of the corresponding region on the plot. In this talk, we will introduce the persistence terrace and demonstrate its ability to detect meaningful features in data.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2017 program

Copyright © American Statistical Association