cancerdetection

cancerdetection - Data Mining Algorithms for Cancer...

This preview shows pages 1–15. Sign up to view the full content.

1 Data Mining Algorithms for Cancer Detection Nirmalya Bandhopadhay, Jun Liu, Sanjay Ranka, Tamer Kahveci http://www.cise.ufl.edu

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

View Full Document
2 Outline • Cancer Datasets are growing - CGH, Microarray, Microarray time course • Datasets are High Dimensional – 1000 to 20000 dimensions • Maximum Influence Feature Selection • Biological Pathway Feature Selection • Cancer Progression Modeling
3 Gene copy number The number of copies of genes can vary from person to person. – ~0.4% of the gene copy numbers are different for pairs of people. Variations in copy numbers can alter resistance to disease – EGFR copy number can be higher than normal in Non-small cell lung cancer. Healthy Cancer Lung images (ALA)

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

View Full Document
4 Raw and smoothed CGH data
5 Example CGH dataset 862 genomic intervals in the Progenetix database

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

View Full Document
6 Problem description •Given a new sample, which class does this sample belong to? •Which features should we use to make this decision?
7 Classification with SVM • Consider a two-class, linearly separable classification problem • Many decision boundaries! • The decision boundary should be as far away from the data of both classes as possible – We should maximize the margin, m Class 1 Class 2 m

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

View Full Document
8 Let { x 1 , . .., x n } be our data set and let y i {1,-1} be the class label of x i Maximize J over α i SVM Formulation Similarity between x i and x j •The decision boundary can be constructed as
9 Pairwise similarity measures • Raw measure – Count the number of genomic intervals that both samples have gain (or loss) at that position. Raw = 3

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

View Full Document
10 SVM based on Raw kernel Using SVM with the Raw kernel amounts to solving the following quadratic program The resulting decision function is Maximize J over α i : Use Raw kernel to replace Use Raw kernel to replace Is this cool?
11 Is Raw kernel valid? Not all similarity function can serve as kernel. This requires the underlying kernel matrix M is “positive semi- definite”. M is positive semi-definite if for all vectors v, v T Mv 0

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

View Full Document
12 • Proof: define a function Φ () where Φ : a {1, 0, -1} m b {1, 0} 2m ,where Φ (gain) = Φ (1) = 01 Φ (no-change) = Φ (0) = 00 Φ (loss) = Φ (-1) = 10 – Raw(X, Y) = Φ (X) T Φ (Y) Is Raw kernel valid? X = 0 1 1 0 1 -1 Y = 0 1 0 -1 -1 -1 * * Φ (X) = 0 0 0 1 0 1 0 0 0 1 1 0 Φ (Y) = 0 0 0 1 0 0 1 0 1 0 1 0 * * Raw(X, Y) = 2 Φ (X) T Φ (Y) = 2
13 Raw Kernel is valid! • Raw kernel can be written as Raw(X, Y) = Φ (X) T Φ (Y) • Define a 2m by n matrix • Therefore, Let M denote the Kernel matrix of Raw

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

View Full Document
14 MIFS for multi-class data One-versus-all SVM [1, 2, 31] [3, 4, 12] [5, 8, 15] Sort ranks of features [2, 31, 1] [12, 4, 3] Ranks of features [5, 15, 8] Feature 2 Feature 3 Feature 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 43

cancerdetection - Data Mining Algorithms for Cancer...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online