Meeting Summary for 11/13/08

We began by discussing the different types of matrices (positive definite etc). Some lectures for this are here:

http://www.youtube.com/watch?v=26lLZZz0KGg (Symmetric Matrices and Positive Definiteness)
http://www.youtube.com/watch?v=0sCLv2EQPg8 (Complex Matrices; Fast Fourier Transform)
http://www.youtube.com/watch?v=ZW8NWVyt4rg (Positive Definite Matrices and Minima)

From Gilbert Strang's lecture on SVD, we identified the most important aspects to be the geometric picture(3:00-4:38) and the equations(7:40-17:00). Here is the lecture:

http://www.youtube.com/watch?v=c9271ZFGKrU

Ina would post the Matlab commands for SVD on the blog. We would all look at the ICA/ NCA papers on our own.

For next week, we decided to look at feature selection. A good paper for this is

http://www.cs.waikato.ac.nz/~mhall/HallHolmesTKDE.pdf

Meeting Summary for 11/6/08

We went over PCA and its applications to microarray data (http://sysbio.soe.ucsc.edu/Pubs/psb00.pdf).

For next week we decided to look SVD with each of us looking at specific aspects

Jang : ICA and NCA

Mike : Excerpts of Strang's lecture;
Application :
Alter O, Brown PO, Botstein D. (2000) Singular value decomposition for genome-wide expression data processing and modeling. Proc Natl Acad Sci U S A, 97, 10101-6.

Ina : Matlab Commands for SVD

Archana : Types of Matrices (Definite, Positive Definite etc)

28 October 2008

Today we watched much of Gilbert Strang's lecture #10 from his MIT OpenCourseWare linear algebra course: http://www.youtube.com/watch?v=5GmCIoIMlxk We were interested in the 4 fundamental subspaces which are explained therein.

We began to go over the problems from last time and got through the first 2 or 3 of them. We decided that while it's good to work out problems, they often require a deeper degree of study (and time) than we have available. The goal is to understand the concepts, be able to talk about them, and then know WHERE to dig deeper when necessary.

For next time we split the six exercises from chapter 2 up between us. The exercises are the ones with the solutions, unlike the actual problem set. I'm taking 1 and 2, Archana 3 and 4, and Ina 5 and 6. We'll review them on Thursday and set a direction for the weekend and next week.

Oct 22 Summary

Discussed orthogonality and orthogonalization process.
Reviewed Gaussian Elimination and well-known types of matrices from
http://math.asu.edu/~bdw/MAT520/Fa98/L2/lect2b.html
http://math.asu.edu/~bdw/MAT520/Fa98/L2/lect2c.html
Will solve following problems next time-
GS: 2.2, 2.4, 2.10, 2.14, 2.15, 2.17, 2.24, 2.27, 2.28, 2.32.