Mathematical Modeling and Numerical Methods
Math 350, Spring 2008

• Course Syllabus
• Course Text (to be posted)
1. Chapter 2 (Introduction and Data)
2. Chapter 3 (Learning)
3. Chapter 4 (Statistics/Linear Regression, in PDF format)
4. Chapter 5 (Linear Alg)
5. Appendix on Derivatives (in PDF format)
6. First part of Chapter 6 (The Best Basis)
7. Second part of Chapter 6 (Eigenfaces)
8. Chapter 7 (Best Non-Orthogonal Basis)
9. Chapter 8: Local Basis and Dimension (future chapter)
10. Chapter 9: Data Clustering
11. Chapter 10: Linear Networks
12. Chapter 11: Radial Basis Functions (new version, updated April 15, 2008). Here is a copy of the old version, if needed.
13. Chapter 12, part 1

Coursework

1. Jan 14-18: Work through Chapters 2 and start 3.
   • Tuesday: Problems 2, 5, 7 (p. 16) and read to page 29
   • Thursday: Exercise 1, p. 29 and Exercise 3, p. 30
   • Friday: Intro to Matlab (Meet in the Computer Lab)
     • Intro to Matlab
     Homework: Pg. 9-10, exercises 5-8. Pg. 14, Exercises 7, 8.
     • Summary of Matlab Commands
   
   
2. Jan 21-25
• Tuesday:
  • Notes about running the n-armed bandit
  • The Matlab function "banditE" (Right-click the mouse here and "Save Link As...")
  • Driver script for the banditE program.
• Thursday: Exercises 1-5, pg. 38
• Friday: Exercises 1-5, p. 44


3. Jan 28-Feb 1: Finish up Chapter 3 (Learning), Start Chapter 5 (Linear Algebra)
• Tuesday: Last page of notes, code up the classification (Use the code below as a template)
  Download and run this Matlab Code (Hebb01.m) for pgs. 46-49
  M-file for class
• Thursday: Exercises 1-7, p 75 (in Ch 5)
• Friday:
  Take Home Quiz (Quiz 2)
  Right-click and "Save Link As...". Print your solution (we'll talk about how in class on Friday) and turn it in on/before class on Tuesday.




4. Feb 4-8: Finish up Chapter 5 (Linear Algebra)
• Tuesday: Finish Problem 6, p. 76. Do Exercise 19, p. 79 (this is a Matlab exercise). Be sure you understand the code!
• Thursday: Homework on this handout. Also, read through to p. 87
• Friday: Appendix on Derivatives (See the link to the text above, also handed out in class). Work through the 8 exercises, p. 240-241.


5. Feb 11-15: We'll be working through Chapter 4, Statistics
• Tuesday: Derivatives, p. 240-1 (We're a little behind).
• Thursday: Statistics (Chapter 4), p. 12-15 (Problems 1-12)
• Friday: HW: Finish up the stats stuff. Quiz 4 handouts below:
  • Quiz 4
  • Data for Quiz 4 (TestData1.mat). Be sure to right-click this link and "Save Link As..."
  • Script Template to use for Quiz 4, Question 2


6. Feb 18-22: Finish Chapter 4, Review for Exam I
• Tuesday:
• Thursday: Review for Exam I
• Friday: Exam I. See the section below for the take home exam materials (Due Tuesday at the beginning of class)


7. Feb 25-29: The Best Basis, Eigenfaces
   • Tuesday: New notes, Chapter 6 (linked above). Read over the section.
   • Thursday: In class exercises today. The "quiz" will be to write up your solutions to these homework problems and turn them in on Tuesday.
   Some Errors/Clarifications from the Homework Sheet
   • Friday: Computer Lab materials:
     1. An set of points for today's lab (900 points in the plane in an elliptical shape) Be sure to right-click the mouse to "Save Link As..."
     2. Computer Lab Here
   
   
8. Mar 3-7:
   • Tuesday: We're working in the lab today. Finish up the quiz from last time, and there is some new Matlab code to look at HERE. You will want to think about it before Friday, and we'll test it on some "movie data", which represents 109 frames, each 120x 160 (so matrix Y1 is 19200 x 109)
   • Thursday: The Best Non-Orthogonal Basis (See the Chapter 7 link above)
     • Example 1: Three dimensional data (ICAexample1.m)
     • Example 2: Handel's Messiah and Laughter (ICAExample2.m)
   • Friday: Quiz 6- We'll meet in the computer lab.
     The data for the quiz: Faces.mat
     
   
   
9. Spring Break
   
10. Mar 24 - Mar 28: Data Clustering.
    • Tuesday: LBG Algorithm. HW: Pg. 133, 1-5
      • Euclidean Distance Matrix function (edm.m)
      • LBG Update function (lbgUpdate.m)
      • Example- How to use the previous functions
      • Second example (in class)
      • Third example (in class)
      • Fourth example(in class)
    • Thursday: Kohonen's Map. HW: Read pgs 135-138. Type in Example 9, p. 138. A new version of Exercise 12, p. 139 is given below.
      • Data set for the examples
      • Script file 1 (SOM1.m)
      • Script file 2 (SOM2.m)
      • New version of Project 12, p. 139 (Requires the 4 files linked below)
      • Taxonomy Data (tax001.m) Type tax001 in the command window to load the data (after downloading this file, of course).
      • Animal names for the data in tax001 (labels.m) You will need this file to run the file below.
      • A function to visualize the centers using the animal names and voronoi partitions (plotcell.m)
      • The script file to make everything work (driverSOM.m)
    • Friday: LBG/SOM in the Lab. The Quiz:
      1. Basic SOM script file (Download and run as an example)
      2. Quiz 7 Questions
      3. Iris data
      4. M-File template for the Iris clustering
      5. The files for the taxonomy question are in the links from Thursday's class.
11. Mar 31 - Apr 4:
    • Tuesday: HW: Consider the Neural Gas code.
    • Thursday: For homework, use the Neural Gas algorithm on (i) a random set of 300 points in the plane, (ii) repeat the experiment from class, and (iii) The boundary problem (page 147) (iv) re-write the code so that there are no graphics.
      1. Neural Gas code (NeuralGas.m)
      2. Example data from class (Data6.mat)
      3. Plotting routine for the example from class (plotNG.m)
      4. Obstacle course data (obstacle1.mat), pg. 147 from notes
    • Friday: The quiz today is mostly homework. We'll spend a little time in class setting up problems 3 and 4. Due on Tuesday.
      • Quiz 8 Instructions
      • Code for HW/Quiz: LinearNet.m
      • Code for HW/Quiz: lag.m
      • Template Script file for Problem 3: Quiz8Prob3.m
      • Template Script file for Problem 4: Quiz8Prob4.m
12. Apr 7 - Apr 11: Radial Basis Functions
    • Tuesday: HW is p. 173: 3, 4, 5, p. 176: 1-3; p. 179 1-6 (if we get there)
      Class Example Links:
      • Function: vander1.m
      • Sample Interpolation 1 (SampleInterp1.m)
      • Sample Interpolation 2
    • Thursday: HW: Continue with previous HW.
      Class Example Links:
      • Exercise 3, p 176
      • EDM Interpolation (Linear)
      • EDM Interpolation (Nonlinear)
    • Friday: Quiz 9 is here
      Here is the new code from today's session:
      • rbf1.m, code for applying nonlinearities by number
      • Example code (rbfError2d.m) to show how accuracy and generalization tend to be competing goals. The accuracy on the training set always goes to zero, but if you use too many centers, the error on the testing set begins to increase.
13. Apr 14 - Apr 18: Nonlinear Networks
    • Tuesday: No classes (Undergraduate Conference)
    • Thursday: Orthogonal Least Squares (Chapter 11, continued).
      Homework: Be sure you can justify/prove items 4, 5, 9, 13, 18 on pages 184-189, and can read/understand the Matlab code.
      Sample training session on two dimensional data using Matlab's built-in functions
    • Friday: Quiz 10
      Matlab Files for the quiz:
      Template for bestdir.m
      Template for olsTest1.m
      Template for convertNet.m
      Script to test previous file, convertTest.m
14. Apr 21 - Apr 25
    • Tuesday: Some feedfoward nets (See the text link above).
      Iris Classification Script 1
      Iris Classification Script 2
    • Thursday: Review for Exam 2. Review Questions Here
    • Friday: Exam 2 See links below for the take home portion of Exam 2
15. Apr 28 - May 2:
    • Tuesday: Feedforward Neural Networks. Homework set 1
      Sigmoidal function (sigma.m)
      Backprop long hand (testbackprop0.m)
      
    • Thursday: Backpropagation, Class Notes
      
      • Character Recognition files (fun to try out!). The main code is appcr1.m, which is built-in to Matlab (type appcr1 in the command window). Once trained, use file alpha_test.m to run through a few test characters.
      • alpha_test.m
      • vectoalpha.m (For making the vectors into arrays)
    • Friday: No regular class today- Try running the script file below (and the alphabet code above) in preparation for the final project. Feel free to ask me any questions on these samples.
    The Leopard (explanation of the problem)
    • The Leopard image (leopard.jpg)
    • Script file to do the texture training.
16. May 6: No class- Work on the Final Exam.
17. May 8th: Final Exam due at 5PM- No exceptions.