Estimating mutual information using B-spline functions – an improved similarity measure for analysing gene expression data

BACKGROUND: The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. In the context of the clustering of genes with similar patterns of expression it has been suggested as a general quantity of similarity to extend commonly used linear measures. Since mutual information is defined in terms of discrete variables, its application to continuous data requires the use of binning procedures, which can lead to significant numerical errors for datasets of small or moderate size. RESULTS: In this work, we propose a method for the numerical estimation of mutual information from continuous data. We investigate the characteristic properties arising from the application of our algorithm and show that our approach outperforms commonly used algorithms: The significance, as a measure of the power of distinction from random correlation, is significantly increased. This concept is subsequently illustrated on two large-scale gene expression datasets and the results are compared to those obtained using other similarity measures. A C++ source code of our algorithm is available for non-commercial use from [email protected] upon request. CONCLUSION: The utilisation of mutual information as similarity measure enables the detection of non-linear correlations in gene expression datasets. Frequently applied linear correlation measures, which are often used on an ad-hoc basis without further justification, are thereby extended

A systematic comparison of genome-scale clustering algorithms

Background: A wealth of clustering algorithms has been applied to gene co-expression experiments. These algorithms cover a broad range of approaches, from conventional techniques such as k-means and hierarchical clustering, to graphical approaches such as k-clique communities, weighted gene co-expression networks (WGCNA) and paraclique. Comparison of these methods to evaluate their relative effectiveness provides guidance to algorithm selection, development and implementation. Most prior work on comparative clustering evaluation has focused on parametric methods. Graph theoretical methods are recent additions to the tool set for the global analysis and decomposition of microarray co-expression matrices that have not generally been included in earlier methodological comparisons. In the present study, a variety of parametric and graph theoretical clustering algorithms are compared using well-characterized transcriptomic data at a genome scale from Saccharomyces cerevisiae. Methods: For each clustering method under study, a variety of parameters were tested. Jaccard similarity was used to measure each clusters agreement with every GO and KEGG annotation set, and the highest Jaccard score was assigned to the cluster. Clusters were grouped into small, medium, and large bins, and the Jaccard score of the top five scoring clusters in each bin were averaged and reported as the best average top 5 (BAT5) score for the particular method. Results: Clusters produced by each method were evaluated based upon the positive match to known pathways. This produces a readily interpretable ranking of the relative effectiveness of clustering on the genes. Methods were also tested to determine whether they were able to identify clusters consistent with those identified by other clustering methods. Conclusions: Validation of clusters against known gene classifications demonstrate that for this data, graph-based techniques outperform conventional clustering approaches, suggesting that further development and application of combinatorial strategies is warranted