Model order selection for biomolecular data clustering
Alberto Bertoni and Giorgio Valentini
Cluster analysis has been widely applied for investigating structure in bio-molecular data. A drawback of most clustering algorithms is that they cannot automatically detect the "natural" number of clusters underlying the data, and in many cases we have no enough "a priori" biological knowledge to evaluate both the number of clusters as well as their validity. Recently several methods based on the concept of stability have been proposed to estimate the "optimal" number of clusters, but despite their successful application to the analysis of complex bio-molecular data, the assessment of the statistical significance of the discovered clustering solutions and the detection of multiple structures simultaneously present in high-dimensional bio-molecular data are still major problems.
We propose a stability method based on randomized maps that exploits the high-dimensionality and relatively low cardinality that characterize bio-molecular data, by selecting subsets of randomized linear combinations of the input variables, and by using stability indices based on the overall distribution of similarity measures between multiple pairs of clusterings performed on the randomly projected data. A χ2-based statistical test is proposed to assess the significance of the clustering solutions and to detect significant and if possible multi-level structures simultaneously present in the data (e.g. hierarchical structures).
The experimental results show that our model order selection methods are competitive with other state-of-the-art stability based algorithms and are able to detect multiple levels of structure underlying both synthetic and gene expression data.