Knowledge-based Analysis of Microarray Gene Expression Data using Support Vector Machines

1. Knowledge-based Analysis of Microarray Gene Expression Data using Support Vector Machines Michael P. S. Brown, William Noble Grundy, David Lin, Nello Cristianini, Charles Sugnet, Terrence S. Furey, Manuel Ares, Jr. David Haussler Proceedings of the National Academy of Sciences. 2000

2. Overview • Objective: Classify genes based on functionality • Observation: Genes of similar function yield similar expression pattern in microarray hybridization experiments • Method: Use SVM to build classifiers, using microarray gene expression data.

3. Previous Methods • Most current methods employ unsupervised learning methods (at the time of the publication) • Genes are grouped using clustering algorithms based on a distance measure • Hierarchical clustering • Self-organizing maps

4. DNA Microarray Data • Each data point represents the ratio of expression levels of a particular gene in an experimental condition and a reference condition • n genes on a single chip • m experiments performed • The results is an n by m matrix of expression-level ratios m experiments m-element expression vector for a single gene n genes

5. DNA Microarray Data • Normalized logarithmic ratio • For gene X, in experience i, define: • Ei is the expression level in the experiment • Ri is the expression level in the reference state • Xi=(x1, x2,..., xn) is the normalized logarithmic ratio • Xi is positive when the gene is induced (turned up) • Xi is negative when the gene is repressed (turned down)

6. Support Vector Machines • Searches for a hyperplane that • Maximizes the margin • Minimizes the violation of the margin * Edda Leopold† and Jörg Kindermann

7. Linear Inseparability • What if data points are not linearly separable? * Andrew W. Moore

8. Linear Inseparability • Map the data to higher-dimension space * Andrew W. Moore

9. Linear Inseparability • Problems with mapping data to higher-dimension space • Overfitting • SVM chooses the maximum margin, and deals well with overfitting • High computational cost • SVM kernels only involve dot products between points (cheap!)

10. SVM Kernels • K(X, Y) is function that calculates a measure of similarity between X and Y • Dot product • K(X,Y) = X.Y • Simplest kernel. Linear hyperplane • Degree d polynomials • K(X,Y) = (X.Y + 1)d • Gaussian • K(X,Y) = exp(-|X - Y|2/22)

11. Experimental Dataset • Expression data from the budding yeast • 2467 genes (n) • 79 experiments (m) • Dataset available on Stanford web site • Six functional classes • From the Munich Information Centre for Protein Sequences Yeast Genome Database • Class definitions come from biochemical and genetic studies • Training data: • positive labels: set of genes that have a common function • Negative labels: set of genes known not to be a member of this function class

12. Experimental Design • Compare the performance of • SVM (with degree 1 kernel, i.e. linear)) • SVM (with degree 2 kernel) • SVM (with degree 3 kernel) • SVM (Gaussian) • Parzen Windows • Fisher’s Linear Discriminate • C4.5 Decision Trees • MOC1 Decision Trees

13. Experimental Design • Define the cost of method M • C(M) = fp(M) + 2.fn(M) • False negatives are weighted higher because the number of true negatives is larger • Cost of each method is compared to: • C(N) = cost of classifying everything as negative • Cost saving of method M is : • S(M) = C(N) - C(M)

14. Experimental Results • SVMs outperform other methods • All classifiers fail to recognize the HTH protein • this is expected • Members of this class are not “similarly regulated”

15. Consistently Misclassified Genes • 20 genes are consistently misclassified by 4 SVM kernels, in different experiments • Difference between the expression data and definitions based on protein structures. • Many of the false positives are known to be important for the functional class (even though they are not included as part of the class)