1. Using SVM for Expression Micro-array Data Mining
—— Data Mining Final Project
Chong Shou
Apr.17, 2007

2. Expression Micro-arrays

3. Expression Micro-arrays
Data:
A n*m data matrix
n = : gene number under investigation
m = 79: conditions under which gene expression levels are measured
Expression level: expression under a certain condition is compared to a reference expression level, positive if up-regulated, negative if down-regulated

4. Expression Micro-arrays
It is believed that genes working together in certain biological processes should have similar expression patterns
We should be able to find similar patterns of genes having related functions
We could use this information to infer (predict) functions of unknown genes

5. Supervised Learning
We use biological knowledge gathered from experiments to label selected genes to a set of classes as our training set
Training set: 2467 genes
Test set: 3754 genes

6. GO (Gene Ontology) Use GO as functional annotation for selected genes
Classes:
Respiration
TCA cycle (biochemical process that produce energy)
Histone (protein helps DNA packing)
Ribosome (protein complex assembles amino acids to proteins)
Proteolysis (process destroy proteins)
Meiosis (process produce reproductive cells)

7. Advantages using SVM Classical supervised learning method
Able to use a variety of distance functions (kernels)
Able to handle data with extremely high dimensions: 79 conditions

8. Details in SVM Parameters
Four kernel functions
Linear
K(X,Y) = <X,Y> + 1
Polynomial
K(X,Y) = (<X,Y> + 1)2
K(X,Y) = (<X,Y> + 1)3
Radial
K(X,Y) = exp(-σ||X - Y||2)

9. Kernel Matrix Modification
Using kernel functions to calculate kernel matrix for the use of SVM training
Ki,j = K(Xi, Xj)
Problem
Positive samples: only a few genes have classification to the six classes
Negative samples: most genes do not have specification classification
Positive samples are considered as noise, thus prone to make incorrect classifications

10. Kernel Matrix Modification (cont)
Add to the diagonal of the kernel matrix a constant whose magnitude depends on the class of the data point, thus control the misclassifications
Positive samples: Kii = Kii + λ(n+/N)
Negative samples: Kii = Kii + λ(n-/N)
λ= 0.1
n+: number of positive samples
n-: number of negative samples
N: total number of samples

11. Othre Supervised Learning Methods
Classification tree
rpart
moc
k-Nearest Neighbors

12. Model Evaluation Confusion Matrix Cost Function Save Function
FP, FN, TP, TN
Cost Function
CM = FPM + 2*FNM
M: learning method
FN has larger weight
Save Function
SM = CN – CM
CN: cost if all samples are labeled negative
Models with large SM are preferred

13. Prediction Use SVM on testing set to predict gene function
Compare the classification result with GO

14. Some Problems
High data matrix dimension, 2467 * 2467 for the training set. Requires long running time on PC.
“predict” function in R

15. Questions?