MATH 250: Mathematical Data Visualization
San Jose State University, Spring 2023Course description [syllabus]
This is a graduatelevel course on dimension reduction and data visualization. Dimensionality reduction methods to be covered include PCA, MDS, ISOmap, LLE, Laplacian Eigenmaps, and LDA. The course is 70% theory (linear algebra) and 30% programming (for matrix computing and data plotting).Textbook
There is no required textbook, but the instructor will provide notes on each covered topic.
The following are recommended readings for further learning:
 Probabilistic Machine Learning: An Introduction [draft copy], by Kevin Patrick Murphy. MIT Press, March 2022.
 Foundations of Data Science [January 2018 version], Avrim Blum, John Hopcroft, and Ravindran Kannan. Cambridge University Press; 1st edition (January 1, 2020).
Technology and equipment requirements
 Canvas: Zoom recordings, assignments and grades will be posted in Canvas (accessible via http://one.sjsu.edu/).
 Piazza: The class will use Piazza as the bulletin board. Please post all courserelated questions there.
 Computing: The course uses MATLAB as the main programming software.
 Equipment: Students should have access to a scanner (physical or cell phone app) in order to scan and submit their work.
Course progress
Slides are being continuously updated from Spring 2022. You are suggested to download a new copy right before each class (remember to refresh your browser).
Date  Lecture Slides  Additional Resources  Homework Assignments 

1/25 
Course introduction and overview [slides] 
[Math 39 webpage] [MATLAB Onramp] 
Hw0 (Due: 2/2, Thurs., 11:59pm) 
1/30 
Basic matrix algebra [slides] 
[Instructor's notes]  Hw1 (See Canvas) 
2/8 
Matrix computing in MATLAB [slides] 
Hw2  
2/15 
Data sets and their visualization in 3D [slides] 
Hw3 

2/22  [Prof. Croot's notes] [MATLAB demonstration]  Hw4  
3/1 
Singular value decomposition [slides] 
[Stanford CS168 lecture on matrix SVD]  Hw5 
3/8 
Generalized inverse and pseudoinverse [slides] 
Hw6  
3/22 
Matrix norm and lowrank approximation [slides] 
Hw7  
4/12 
Principal component analysis (PCA) [slides] 
Hw8  
5/3 
Linear discriminant analysis (LDA) [slides] 
Hw9  
5/10 
Multidimensional Scaling (MDS) [slides] 
Hw10 (optional)  
skipped 
ISOmap [slides] 
Hw9 (see Canvas)  
skipped 
Laplacian Eigenmaps [slides] 
Hw10 (see Canvas) 
More learning resources
MATLAB resources
 MATLAB Onramp
 MATLAB Fundamentals
 Introduction to Linear Algebra with MATLAB
 MATLAB for Data Processing and Visualization
 MATLAB Programming Techniques
 Statistics and Machine Learning Toolbox
 MATLAB Basic Functions Reference
Data sets
 20 Newsgroups Data [data] [website]
 MNIST Handwritten Digits [data] [website]
 FashionMNIST
 USPS Zip Code Data
 Wine Quality Data Set
 UCI Machine Learning Repository
 Extended Yale Face Database B
 Oxford Flowers Category Datasets
Useful course websites
 Prof. Veksler's CS9840a Learning and Computer Vision at University of Western Ontario
 Andrew Ng's CS 229 Machine Learning at Standford University
 Manik's CSL 864  Special Topics in AI: Classification at Microsoft