Locally Linear Embedding (LLE) -- theoretical analysis and new results, part 1

Welcome to Part 1 of a 5-part lecture series exploring recent advancements and insights into Locally Linear Embedding (LLE), one of the first nonlinear dimensional reduction algorithms introduced in 2000. This series provides a range of theoretical analyses from various perspectives, offering a thorough understanding of this foundational technique that we know up to now (2025-1-2).

This first part introduces the algorithm itself and presents a framework for analyzing it within the context of the manifold model.