MATH 250: Mathematical Data Visualization
San Jose State University, Spring 2023
Course description [syllabus]
This is a graduate-level 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 course-related 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 low-rank 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]
- Fashion-MNIST
- 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