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A Combinatorial Approach to the Analysis of Differential Gene
Expression Data
The Use of Graph Algorithms for Disease Prediction and Screening
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The Goal
• To classify patients based on expression profiles– Presence of cancer– Type of cancer– Response to treatment
• To identify the genes required for accurate classification– Too many = unnecessary noise– Too few = insufficient information
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Classic Clustering Problem
• Current techniques:– Hierarchical Clustering– K-Means Clustering– Self-Organizing Maps– Others
• Drawbacks:– Determining cluster boundaries difficult with diffuse
data– Objects can only belong to one group
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Eliminate Poorly Covering Genes
Raw Data
Set of Discriminatory Genes
Gene Scores
Verify by Classification
Calculate Sample Similarities
Apply Threshold
Eliminate PoorlyDiscriminating Genes
Algorithmic Training
Dominating Set
Maximal Cliques
Gene Scoring
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Raw Data
Eliminate PoorlyDiscriminating Genes
Algorithmic Training
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The Gene Scoring Function: Identifying Discriminators
0 2 4 6 8 10 0 2 4 6 8
score(genei) mclassA mclassB classA classB
vs.
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Eliminate Poorly Covering Genes
Raw Data
Eliminate PoorlyDiscriminating Genes
Algorithmic Training
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Eliminate Poorly Covering GenesSamples Genes
Cla
ss 2
Cla
ss 1
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Eliminate Poorly Covering Genes
Raw Data
Calculate Sample Similarities
Apply Threshold
Eliminate PoorlyDiscriminating Genes
Algorithmic Training
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Create Unweighted Graph
• Complete, edge-weighted graph– Vertices = samples– Edge weight = similarity metric
• Remove edge weights– If edge weight < threshold, remove edge from
graph– Otherwise, keep edge, ignore weight
• Result: incomplete unweighted graph
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The Edge Weight Function
score(genei) (1 expression_valueij expression_valueik )
where,expression valueij = expression value of genei for samplej
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Eliminate Poorly Covering Genes
Raw Data
Set of Discriminatory Genes
Gene Scores
Verify by Classification
Calculate Sample Similarities
Apply Threshold
Eliminate PoorlyDiscriminating Genes
Algorithmic Training
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• A completely connected subset of vertices in a graph
• Maximal clique = local optimization• NP-complete
What is a Clique?
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Classification Using Clique
Class2
Class 1
Class 1
Class 3
Class 2
GRAPH
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A Selection of Discriminators
ADH1B alcohol dehydrogenase IB alcohol dehydrogenase activity
FHL1 four and a half LIM domains 1 cell growth, cell differentiation
HBB hemoglobin, beta oxygen transport
CYP4B1 cytochrome P450 4B1 electron transport
TNA tetranectin plasminogen binding protein
TGFBR2 transforming growth factor, beta receptor II
transmembrane receptor protein serine/threonine kinase signaling pathway
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Raw Data
Classify Unknown Samples
Calculate Sample Similarities
Apply Threshold
Set of Discriminatory Genes, Scores
The Algorithm - Unsupervised
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Summary
• Intersection of clique and dominating set techniques improves results
• Combined orthogonal scoring identifies limited number of discriminatory genes
• Clique offers means of validating obtained scores and weights
• Our technique identifies differing set of discriminatory genes from original paper
• Clique-based classification a viable complement to present clustering methods
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Ongoing and Future Research
• Reverse Training• Train to distinguish among types of cancer• Experiment with different weight functions (ex.
Pearson’s coefficient)• Investigate using less stringent techniques
– Near-cliques – Neighborhood search– K-dense subgraphs
• Port codes to SGI Altix supercomputer
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Our Research Group
Mike Langston, Ph. D.
Lan Lin Chris SymonsXinxia Peng Bing Zhang, Ph.
D.
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