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)

5 November 2008

We viewed Dr. Gilbert Strang's Linear Algebra lecture (#21) on EigenValue and EigenVectors through MIT OpenCourseware. Ina then ran through a brief tutorial on matlab for functions for calculating eigenvalues and eigenvectors. The tutorials referred to are as under:
1.http://mit.ocw.universia.net/14.452/s02/pdf/MatlabTut.pdf
2.http://amath.colorado.edu/computing/Matlab/Tutorial/LinAlgebra.html

31 October 2008

Today we concluded our introduction to linear algebra with a distribution of Jieping Ye's Basics of Lineal Algebra Matrices handout:

http://www.public.asu.edu/~jye02/CLASSES/Fall-2007/NOTES/Basics-Matrix.pdf

His other class materials are also available here:

http://www.public.asu.edu/~jye02/CLASSES/Fall-2007/index.htm

For next week, we will discuss Eigenvectors and Eigenvalues in the context of Principle Components Analysis with bioinformatics applications. Archana and Jang will locate 2-4 papers including overview information for PCA, ICA and NCA (just a little on independent and network component analysis). Ina will find Matlab tutorial information for eigenvalues, eigenvectors and PCA computation. Mike will find video lecture introductory materials for eigenvectors and eigenvalues.

On Tuesday we will watch and discuss the lecture and Ina will give a Matlab demo for computing eigenvalues and eigenvectors. On Thursday we will discuss the papers we've all been reading all week, and conclude with a tutorial computation of principle components from a biomedical dataset.

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.

09 October Summary

Continuing on Regression study, we discussed degrees of freedom in different estimators and error sum of squares calculations. We then looked at Coefficient of Determination and discussed its use/application in Regression analysis and its application with respect to gene expression data study. For next week we will be reading the paper by Dougherty et. al on CoD relevant to our work. Archana gave us a brief overview on estimation by maximum likelihood and went through the formulas used to derive the maximum-likelihood estimators.
Next week we will also discuss the first 2 chapters in Linear Algebra by Prof. Gilbert Strang, namely :
1. Matrices and Gaussian Elimination
2. Vector Spaces.

Online lectures of his are available at : http://web.mit.edu/18.06/www/Video/video-fall-99-new.html