
Mathematics for Data Science (数据中的数学) 
Course Information 
This course is open to graduates and senior undergraduates in applied mathematics and statistics who are involved in dealing with data. It covers some topics on high
dimensional statistics, manifold learning, diffusion geometry, random walks on graphs, concentration of measure, random matrix theory, geometric and topological methods, etc.
Prerequisite: linear algebra, basic probability and multivariate statistics, basic stochastic process (Markov chains).
Tue 10:1012:00pm;
Fri (odd weeks) 10:1012:00pm
(Possibly change later!) Rm 425, Ying Jie Exchange Center; 数院本科生机房, 英杰交流中心 425
We are targeting biweekly homeworks with miniprojects, and a final major project. No final exam. Scribers will get bonus credit for their wonderful work!
YAN, Bowei (闫博巍) Email: bwyan (add "AT pku DOT edu DOT cn" afterwards)
Date  Topic  Instructor  Scriber 
09/06/2011, Tue  Lecture 01: Introduction: Data Representation, Sample Mean, Variance, and PCA [lecture note 1.pdf]

Y.Y.  Yan, Bowei 
09/09/2011, Fri  Lecture 02: Stein's Phenomenon and Shrinkage [lecture note 2 by Sheng,Hu.pdf]

Y.Y.  Sheng, Hu. Luo, Wulin. Lv, Yuan. 
09/13/2011, Tue  Lecture 03: Random Matrix Theory and PCA [lecture note 3.pdf]

Y.Y.  Tengyuan Liang; Bowei Yan 
09/20/2011, Tue  Lecture 04: Diffusion Map, an introduction [lecture note 4.pdf, version 2]

Xiuyuan Cheng Princeton 
Peng Luo; Wei Jin 
09/23/2011, Fri  Lecture 05: Diffusion Map, convergence theory [lecture note 5.pdf, version 4]

Xiuyuan Cheng Princeton 
Jun Yin; Ya'ning Liu 
09/27/2011, Tue  Lecture 06: Diffusion Distance [lecture note 6.pdf]

Y.Y.  Lei Huang; Yue Zhao 
10/11/2011, Tue  Lecture 07: Random Walk on Graphs: PerronFrobenius Vector and PageRank [lecture note 7.pdf]

Y.Y.  Yuan Lu; Bowei Yan 
10/18/2011, Tue  Lecture 08: Random Walk on Graphs: Fiedler Vector, Cheeger inequality and spectral bipartition [lecture note 8.pdf]

Y.Y.  Zhiming Wang; Feng Lin 
10/21/2011, Fri  Lecture 9: Random Walk on Graphs: Lumpability (metastability), piecewise constant right Eigenvectors and Multiple Spectral Clustering (MNcut) [lecture note 9.pdf]

Y.Y.  Hong Cheng; Ping Qin 
10/25/2011, Tue  Lecture 10: Random Walk on Graphs: Diffusion Distance and Commute Time Distance [lecture note 10.pdf]

Y.Y.  Tangjie Lv; Longlong Jiang 
11/01/2011, Tue  Lecture 11: PCA vs. MDS: Schoenberg Theory

Y.Y.  Yanzhen Deng; Jie Ren 
11/04/2011, Fri  Lecture 12: Random Projections and Metric: JohnsonLindenstrauss Theory

Y.Y.  
11/08/2011, Tue  Lecture 13: MDS with uncertainty: Graph Realization

Y.Y.  
11/15/2011, Tue  Lecture 14: Manifold Learning (Nonlinear Dimensionality Reduction): ISOMAP vs. LLE

Y.Y.  
11/18/2011, Fri  Lecture 15: Other Manifold Learning Techniques: Laplacian, Hessian, LTSA

Y.Y.  
11/22/2011, Tue  Lecture 16: Multiscale SVD and Wavelets on Graphs

Y.Y.  
11/29/2011, Tue  Lecture 17: Sparsity in High Dimensional Statistics

Y.Y.  
12/02/2011, Fri  Lecture 18:

Weinan E  
12/06/2011, Tue  Lecture 19:

Weinan E  
12/13/2011, Tue  Lecture 20:

Y.Y.  
12/16/2011, Fri  Lecture 21:

Y.Y.  
12/20/2011, Tue  Lecture 22: Final Project Report

Y.Y. 