Geometric problems in manifold learning
陳志偉教授國立中山大學應用數學系 3:30 p.m. – 5:00 p.m. 鴻經館M107Abstract：
Manifold learning(ML) is a branch of machine learning, which is used to do clustering, visualization, and nonlinear dimensionality reduction, etc. Roughly speaking, ML is to "learn the invisible manifold by embedding a whole lot of sample points in it into the plane or the space." Since 2000, graph theory and spectral methods have been greatly used in the algorithms of ML. When the number of sample points is getting larger and larger, the graph constructed by sample points shall converge to the manifold. To understand the limiting behavior and thus justify the algorithms, tools from differential geometry, PDE, or functional analysis must be involved. In this talk, I will give some concrete examples to demonstrate how geometry plays a role in this theoretical analysis of ML.