MATH 253: Mathematical Methods for Data Visualization

San Jose State University, Spring 2020

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Course description [Syllabus]

This is a graduate course on dimension reduction for the purpose of data visualization. The course is 70% theory (linear algebra) and 30% programming (for matrix computing and data plotting).

Topics to be covered include:

1. Programming basics and high quality data plotting in 3D
2. Advanced linear algbera
3. Dimension reduction techniques
• Principal component analysis
• Multidimensional scaling
• ISOmap
• Laplacian eigenmaps
• Fisher linear discriminant
4. Introduction to clustering

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Textbook

"Foundations of Data Science Hardcover" [Unofficial version], by Avrim Blum, John Hopcroft, and Ravi Kannan, Cambridge University Press (March 12, 2020). We will use Chapter 3 and Appendix 12.8 of the book.

Additionally, the course will rely on the following papers:

• Multidimensional scaling (MDS) 
• ISOmap
• Laplacian eigenmaps

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Course progress

Date	Lecture Slides	Further Reading
1/23	Course introduction and overview [slides]	Course syllabus [MATLAB Onramp]
1/28	Review of linear algebra and multivariable calculus [slides]	Appendix 12.8 of the textbook (p437)
2/4	Matrix computing in MATLAB [slides]  MATLAB scripts: [part 1] [part 2]	[Matrices and Arrays]  [Mathworks linear algebra documentation]
2/11	High quality data plotting in MATLAB [slides]  MATLAB scripts: [part 1] [part 2] [part 3] [part 4]	[Types of MATLAB Plots]  [MATLAB Plot Gallery]
2/20	Rayleigh quotient [slides]	[Prof. Croot's notes] [MATLAB demonstration]
2/25	Singular value decomposition of matrices [slides]	Chapter 3 of textbook
2/27	Generalized inverse and pseudoinverse [slides]	[Chapter 3 of textbook] [Prof. Sawyer's notes] [Prof. Laub's notes]
3/3	Matrix norm and low-rank approximation [slides]	Chapter 3 of textbook
3/16	Principal Component Analysis (PCA) [slides]	Tutorial by J. Shlens
3/26	Multidimensional Scaling (MDS) [slides]	A book chapter on MDS
4/7	ISOmap [slides] [website]	Original paper (Science, 2000)
4/14	Linear Discriminant Analysis (LDA) [slides]	Prof. Olga Veksler’s lecture
4/30	Laplacian Eigenmaps [slides]	Original paper (Neural Computation, 2003)

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More learning resources

Programming languages

• MATLAB:
• MATLAB Onramp
• Common Matlab commands;
• Python:
• Python for data science - learn in 3 days
• Python Introduction and Linear Algebra Review (Stanford lecture)
• NUMPY TUTORIAL WITH EXERCISES
• NumPy for Matlab users
• BEST PANDAS TUTORIAL | LEARN PANDAS WITH 50 EXAMPLES
• Sample codes by D. Sarkar for data visualization
• A Guide to Pandas and Matplotlib for Data Exploration

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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

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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

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Instructor feedback

This is the first time the course is offered at SJSU. Your feedback (as early as possible) is encouraged and greatly appreciated, and will be seriously considered by the instructor for improving the course experience for both you and your classmates. Please submit your annonymous feedback through this page.

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