A robust approach based on Weibull distribution for clustering gene expression data

Abstract

Abstract Background Clustering is a widely used technique for analysis of gene expression data. Most clustering methods group genes based on the distances, while few methods group genes according to the similarities of the distributions of the gene expression levels. Furthermore, as the biological annotation resources accumulated, an increasing number of genes have been annotated into functional categories. As a result, evaluating the performance of clustering methods in terms of the functional consistency of the resulting clusters is of great interest. Results In this paper, we proposed the WDCM (Weibull Distribution-based Clustering Method), a robust approach for clustering gene expression data, in which the gene expressions of individual genes are considered as the random variables following unique Weibull distributions. Our WDCM is based on the concept that the genes with similar expression profiles have similar distribution parameters, and thus the genes are clustered via the Weibull distribution parameters. We used the WDCM to cluster three cancer gene expression data sets from the lung cancer, B-cell follicular lymphoma and bladder carcinoma and obtained well-clustered results. We compared the performance of WDCM with k-means and Self Organizing Map (SOM) using functional annotation information given by the Gene Ontology (GO). The results showed that the functional annotation ratios of WDCM are higher than those of the other methods. We also utilized the external measure Adjusted Rand Index to validate the performance of the WDCM. The comparative results demonstrate that the WDCM provides the better clustering performance compared to k-means and SOM algorithms. The merit of the proposed WDCM is that it can be applied to cluster incomplete gene expression data without imputing the missing values. Moreover, the robustness of WDCM is also evaluated on the incomplete data sets. Conclusions The results demonstrate that our WDCM produces clusters with more consistent functional annotations than the other methods. The WDCM is also verified to be robust and is capable of clustering gene expression data containing a small quantity of missing values.