A Combinatorial Approach to the Analysis of Differential Gene - - PowerPoint PPT Presentation

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 Poorly Discriminating Genes

Algorithmic Training

Dominating Set Maximal Cliques Gene Scoring

Raw Data Eliminate Poorly Discriminating Genes

Algorithmic Training

The Gene Scoring Function: Identifying Discriminators

2 4 6 8 10 2 4 6 8

score(genei) = mclassA − mclassB − σ classA +σ classB

vs.

Eliminate Poorly Covering Genes Raw Data Eliminate Poorly Discriminating Genes

Algorithmic Training

Eliminate Poorly Covering Genes

Samples Genes

Class 2 Class 1

Eliminate Poorly Covering Genes Raw Data Calculate Sample Similarities Apply Threshold Eliminate Poorly Discriminating 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 Poorly Discriminating 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

electron transport cytochrome P450 4B1 CYP4B1 cell growth, cell differentiation four and a half LIM domains 1 FHL1 alcohol dehydrogenase activity alcohol dehydrogenase IB ADH1B

• xygen transport

hemoglobin, beta HBB transmembrane receptor protein serine/threonine kinase signaling pathway transforming growth factor, beta receptor II TGFBR2 plasminogen binding protein tetranectin TNA

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 Symons Xinxia Peng Bing Zhang, Ph. D.