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

Revised Schedule

Revised Schedule

Date	Topic
9/3	Statistical Distributions
9/8	Statistical Distributions
9/10	Normalization
9/15	Normalization
9/17	Hypothesis Testing
9/22	Hypothesis Testing
9/24	Hypothesis Testing
9/30	P-Value Corrections
10/2	Significance Testing
10/7	Regression Analysis
10/9	Regression Analysis
	Matrices, Gaussian Elimination, Vector Spaces (Ch 1&2)
	Matrices, Gaussian Elimination, Vector Spaces (Ch 1&2)
	Orthogonality and Determinants (Ch 3& 4)
	Orthogonality and Determinants (Ch 3& 4)
	Eigenvalue and EigenVectors (Ch5)
	Eigenvalue and EigenVectors (Ch5)
	Positive Definite Matrices (Ch6)
	Computations with Matrices (Ch7) if possible else Ch 6
	Error Estimation
	Error Estimation
	Feature Selection
	Feature Selection
	Kernel Methods (Classification)
	Kernel Methods (Classification)
	EM Optimization (Clustering)
	EM Optimization (Clustering)

07 October Summary

Today we talked mainly about linear regression. Review chapters 1 and 2 in the Montgomery Peck and Vining introduction to linear regression analysis text for next time. Chapter two is posted below.

Also posted are papers relating to GoMiner. We were interested in its use of FDR in reporting significant GO terms from last time.

Finally posted is my ECE 380 capstone project which does a simple linear regression analysis (for an example).

http://www.public.asu.edu/~mverdic/papers

Meeting Summary for 9/30/2008

I spoke about FDR Correction and gave a brief outline of the methods involved in Multiplicity Adjustment and FDR Correction:
Multiplicity/ P Value Adjustment

- Single Step
---Boneferonni
---Sidak

- Step-down
---Holms
---Westfall & Young (min P/ max T)

FDR Correction
---Benjamini & Hochberg

Useful reference for this is : Benjamini & Hochberg 1995, J. Roy. Statist. Soc. Ser. B 57:289-300

Jang went over Hypergeometric tests, Fisher's exact test and its difference with Chi Squared Test.

For the next meeting(Friday instead of Thursday), Mike said he would look at applying Fisher's exact test and FDR Correction(GoMiner).

We also decided we would start off with an introduction to regression.