Colloquium Talk
Robin Belton, Smith College
Thursday, December 14, 2023 at 1PM
Rocky  312

Title: Adaptive Algorithms in Geometric and Topological Visualization

Abstract: Geometry and Topology have been increasingly used to visualize and summarize the “shape” of data. Mapper is a popular topological data visualization tool that takes as input a set of point cloud data and produces as output a graph of vertices and edges reflecting the structure of the underlying data. To use Mapper, the user must specify many parameters to get the output graph. Optimizing these parameters is an essential part of obtaining a nice Mapper graph but are often challenging to find. We focus on the open cover parameter and propose a new algorithm for learning an open cover that is based on clustering algorithms, statistical tests, and an iterative splitting procedure. At the end, we discuss how to extend these ideas to different settings.