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 recoveringa low-dimensional manifold embedded in a high-dimensional ambient space.
The goal of this mini-course is to introduce three of the important topics in manifold learning theory: PCA (Principal Component Analysis), diffusion map and MDS (Multidimensional Scaling). We will introduce the theory and implementation of these topics. The prerequisite of this mini-course is linear algebra.