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

Cost saving of method M is : S(M) = C(N) - C(M)

Experimental Results

SVM (d=1)

SVM (d=2)

SVM (d=3)

SVM(Gauss)

ParzenWindows

Fisher's LD C4.5 MOC1

TCA 6 9 12 11 6 5 -7 -1Resp 31 39 38 33 18 30 8 -4Ribo 224 229 229 226 220 217 169 164Prot 35 48 51 52 39 39 33 26Hist 18 18 18 18 14 16 16 10HTH -56 -3 -1 0 -14 -14 -2 -6

SVMs outperform other methods All classifiers fail to recognize the HTH protein

this is expected Members of this class are not “similarly regulated”

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)