A Combinatorial Approach to the Analysis of Differential Gene

Expression Data

The Use of Graph Algorithms for Disease Prediction and Screening

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

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

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

Raw Data

Eliminate PoorlyDiscriminating Genes

Algorithmic Training

The Gene Scoring Function: Identifying Discriminators

0 2 4 6 8 10 0 2 4 6 8

score(genei) mclassA mclassB classA classB

vs.

Eliminate Poorly Covering Genes

Raw Data

Eliminate PoorlyDiscriminating Genes

Algorithmic Training

Eliminate Poorly Covering GenesSamples Genes

Cla

ss 2

Cla

ss 1

Eliminate Poorly Covering Genes

Raw Data

Calculate Sample Similarities

Apply Threshold

Eliminate PoorlyDiscriminating Genes

Algorithmic Training

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

The Edge Weight Function

score(genei) (1 expression_valueij expression_valueik )

where,expression valueij = expression value of genei for samplej

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

• A completely connected subset of vertices in a graph

• Maximal clique = local optimization• NP-complete

What is a Clique?

Classification Using Clique

Class2

Class 1

Class 1

Class 3

Class 2

GRAPH

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

Raw Data

Classify Unknown Samples

Calculate Sample Similarities

Apply Threshold

Set of Discriminatory Genes, Scores

The Algorithm - Unsupervised

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

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

Our Research Group

Mike Langston, Ph. D.

Lan Lin Chris SymonsXinxia Peng Bing Zhang, Ph.

D.