Extrinsic and Intrinsic Manifold Learning - Old and New

Explore both classical and cutting-edge approaches to manifold learning in this conference talk that examines how to identify and understand geometric structures hidden within data. Learn about extrinsic manifold learning techniques where the underlying manifold is embedded in high-dimensional Euclidean space, including detailed exposition of the foundational work "Testing the manifold hypothesis" developed with collaborators S. Mitter and H. Narayanan. Discover the challenges and methodologies for determining whether data truly lies on a low-dimensional manifold within a larger space. Delve into the emerging field of intrinsic manifold learning, where no embedding assumption is made and researchers work directly with intrinsic distance measurements that have been corrupted by noise. Gain insights into the mathematical frameworks, statistical methods, and computational approaches used to extract meaningful geometric information from noisy, high-dimensional datasets. Understand the theoretical foundations that underpin both classical and modern manifold learning algorithms, and explore how these techniques apply to real-world problems in data analysis, machine learning, and statistical inference.