2011 Summer School at Fudan University

PKU

Fudan Summer School: Mathematics of Data -- Geometric and Topological Methods
Summer 2011

Course Information

Synopsis (摘要)

In the past decade, there emerges a new direction in applied mathematics and statistical machine learning, which tends to exploit some traditional mathematics to capture nonlinear variation of data distribution in high dimensional spaces. Such a perspective includes various geometric embedding techniques, such as the locally linear embedding (LLE), ISOMAP, and diffusion maps etc. Most recently, computational topology techniques also began to enter data science. In this lecture series, we will give a systematic treatment of these techniques, in a broad sense of mathematics of data with an emphasis on geometric and topological approaches. However, the topics discussed here are of highly dynamic, whence the active participation of graduate students are welcome in this direction of research.

Time and Place:

MTuWThF 2:00-4:00pm, Room 307, West Wing Building of Guanghua Towers

Schedule:

Date	Slides
Mon, 07/11/2011	Lecture 01: Geometric Data Analysis: from PCA/MDS to LLE/ISOMAP [slides] 1. [ ISOMAP website ] 2. [ LLE website ]
Tue, 07/12/2011	Lecture 02: Geometric Data Analysis: Diffusion Geometry [slides] 1. matlab codes: mani.m [ download ] 2. Todd Witman's Comparisons of Manifold Learning Techniques [ slides ] 3. [ Dimensionality Reduction Resources at Gatsby ] 4. [ Matlab Toolbox for Dimensionality Reduction ]
Wed, 07/13/2011	Lecture 03: Introduction to Topological Data Analysis [slides] 1. [ Stanford CompTop Website ] where you find preprints and softwares. 2. [ Mapper in RNA Tetraloop ] where you reproduce some experiments for Molecular Dynamics.
Thu, 07/14/2011	Lecture 04: Combinatorial Hodge Theory with Applications [slides] 1. Matlab codes for statistical ranking paper [ download ].
Fri, 07/15/2011	Seminar: HodgeRank on Random Graphs [slides] Abstract. Hodge decomposition can be adapted to analyze edge flows on Erdos-Renyi random graphs, whose edges are selected independently. Such graphs naturally emerge from experimental designs in crowdsourcing ranking on Internet, and exhibit topological phase transitions. Exploiting such phase transitions, Hodge decomposition can be used to infer global ranking efficiently without jeopardizing the accuracy of performance. We will demonstrate a particular application on video quality assessment.