On the Effectiveness of Persistent Homology

Explore the effectiveness of persistent homology in shape analysis tasks through this insightful conference talk. Delve into the reasons behind the success of persistent homology (PH) in Topological Data Analysis and discover its potential in detecting geometric and topological features. Learn about experiments comparing PH to other methods, including PointNet, in tasks such as detecting the number of holes, curvature, and convexity in 2D and 3D point clouds. Gain insights into PH's performance under limited computational resources, limited training data, and out-of-distribution test data. Understand the project description, methodology, and results, followed by a summary and Q&A session. Examine differences in approaches, sources of variation, and examples in higher dimensions. Conclude with a discussion on convexity and random directions, providing a comprehensive overview of persistent homology's applications in natural and applied sciences.