Knowledge-based%20Analysis%20of%20Microarray%20Gene%20Expression%20Data%20using%20Support%20Vector%20Machines

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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
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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.

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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

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Advantages of Supervised Learning and SVMs

• Supervised methods can take advantage of prior
  knowledge
• SVMs are well suited to extremely
  high-dimensional feature space

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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
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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)

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Support Vector Machines

• Searches for a hyperplane that
• Maximizes the margin
• Minimizes the violation of the margin

Edda Leopold and Jörg Kindermann
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Linear Inseparability

• What if data points are not linearly separable?

Andrew W. Moore
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Linear Inseparability

• Map the data to higher-dimension space

Andrew W. Moore
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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!)

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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 - Y2/2?2)

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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

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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
• Fishers Linear Discriminate
• C4.5 Decision Trees
• MOC1 Decision Trees

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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)

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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

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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)