Discovering biclusters in gene expression data based on high-dimensional linear geometries.

Xiangchao Gan,Hong Yan,Alan Wee-Chung Liew

doi:10.1186/1471-2105-9-209

Abstract

BackgroundIn DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. However, in many situations a subset of genes only exhibits consistent pattern over a subset of conditions. Conventional clustering algorithms that deal with the entire row or column in an expression matrix would therefore fail to detect these useful patterns in the data. Recently, biclustering has been proposed to detect a subset of genes exhibiting consistent pattern over a subset of conditions. However, most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Moreover, most of these algorithms can only detect a restricted set of bicluster patterns.ResultsIn this paper, we present a novel geometric perspective for the biclustering problem. The biclustering process is interpreted as the detection of linear geometries in a high dimensional data space. Such a new perspective views biclusters with different patterns as hyperplanes in a high dimensional space, and allows us to handle different types of linear patterns simultaneously by matching a specific set of linear geometries. This geometric viewpoint also inspires us to propose a generic bicluster pattern, i.e. the linear coherent model that unifies the seemingly incompatible additive and multiplicative bicluster models. As a particular realization of our framework, we have implemented a Hough transform-based hyperplane detection algorithm. The experimental results on human lymphoma gene expression dataset show that our algorithm can find biologically significant subsets of genes.ConclusionWe have proposed a novel geometric interpretation of the biclustering problem. We have shown that many common types of bicluster are just different spatial arrangements of hyperplanes in a high dimensional data space. An implementation of the geometric framework using the Fast Hough transform for hyperplane detection can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis.

Highlights

In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification
Similar to the validation method proposed by Tanay et al [10], we investigate whether the gene groups produced by different algorithms show significant enrichment with respect to a specific Gene Ontology (GO) annotation
We presented a novel interpretation of the biclustering problem in terms of the geometric distributions of data points in a high dimensional data space

Summary

Introduction

In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. Most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Most of these algorithms can only detect a restricted set of bicluster patterns. The data to be analyzed often include many heterogeneous conditions from many experiments In these instances, it is often unrealistic to require that related genes behave across all measured conditions and conventional clustering algorithms, such as the k-means and hierarchical clustering algorithms [5,6] and the self-organizing map [7], often cannot produce a satisfactory solution.

Methods

Results

Conclusion