Lect15 Microarray analysis

# An Introduction to Bioinformatics Algorithms (Computational Molecular Biology)

This preview shows pages 1–11. Sign up to view the full content.

L15:Microarray analysis (Classification)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Biological Problem Two conditions that need to be differentiated, (Have different treatments). EX: ALL (Acute Lymphocytic Leukemia) & AML (Acute Myelogenous Leukima) Possibly, the set of genes over-expressed are different in the two conditions
Geometric formulation Each sample is a vector with dimension equal to the number of genes. We have two classes of vectors (AML, ALL), and would like to separate them, if possible, with a hyperplane.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Basic geometry What is | | x | | 2 ? What is x /| | x | | Dot product? x=(x 1 ,x 2 ) y x T y = x 1 y 1 + x 2 y 2 = || x || || y ||cos q x cos q y + || x || || y ||sin( q x )sin( q y ) || x || || y ||cos( q x - q y )
Dot Product Let β be a unit vector. | | β | | = 1 Recall that β T x = | | x| | cos θ What is β T x if x is orthogonal (perpendicular) to β ? θ x β β T x = | | x| | cos θ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hyperplane How can we define a hyperplane L? Find the unit vector that is perpendicular (normal to the hyperplane)
Points on the hyperplane Consider a hyperplane L defined by unit vector β , and distance β 0 from the origin Notes; For all x L, x T β must be the same, x T β = β 0 For any two points x 1 , x 2 , (x 1 - x 2 ) T β =0 Therefore, given a vector β , and an offset β 0 , the hyperplane is the set of all points {x : x T β = β 0 } x 1 x 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hyperplane properties Given an arbitrary point x, what is the distance from x to the plane L? D(x,L) = ( β T x - β 0 ) When are points x1 and x2 on different sides of the hyperplane? x β 0
Hyperplane properties Given an arbitrary point x, what is the distance from x to the plane L? D(x,L) = ( β T x - β 0 ) When are points x 1 and x 2 on different sides of the hyperplane? Ans: If D(x 1 ,L)* D(x 2 ,L) < 0 x β 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Input: A training set of +ve & -ve examples Recall that a hyperplane is represented by {x:- β 0 + β 1 x 1 + β 2 x 2 =0} or (in higher dimensions) {x: β T x- β 0 =0} Goal: Find a hyperplane that ‘separates’ the two classes. Classification: A new point x is +ve if
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 40

Lect15 Microarray analysis - L15:Microarray...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online