Manifold learning encompasses much of the disciplines of geometry, computation, and statistics, and has become an important research topic in data mining and statistical learning. The simplest description of manifold learning is that it is a class of algorithms for recovering a low-dimensional manifold embedded in a high-dimensional ambient space. This course aims to help those who want to understand the geometric aspects of various learning algorithms.

This course focuses on introducing spectral methods for the dimensional reduction problem. Topics include (1) Principal component analysis; (2) Multidimensional scaling; (3) Locally linear embedding; (4) Maximum variance unfolding; (5) Diffusion map and (6) Cluster analysis.

We will introduce the theories and implementations of these topics.