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
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Knowledge-based Analysis of Microarray Gene Expression Data using Support Vector Machines
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. Overview. - PowerPoint PPT Presentation
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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
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.
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
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
n ge
ne
s
m experiments
m-element expression vector for a single gene
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)
Support Vector Machines
* Edda Leopold† and Jörg Kindermann
Searches for a hyperplane that Maximizes the margin Minimizes the violation of the margin
Linear Inseparability What if data points are not linearly
separable?
* Andrew W. Moore
Linear Inseparability Map the data
to higher-dimension space
* Andrew W. Moore
Linear Inseparability
Problems with mapping data to higher-dimension space
1. Overfitting• SVM chooses the maximum margin, and deals
well with overfitting
2. High computational cost• SVM kernels only involve dot products between
points (cheap!)
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|2/22)
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
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
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