title: Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach.
abstract: BACKGROUND
  Biologists often employ clustering techniques in the explorative phase of microarray data analysis to discover relevant biological groupings. Given the availability of numerous clustering algorithms in the machine-learning literature, an user might want to select one that performs the best for his/her data set or application. While various validation measures have been proposed over the years to judge the quality of clusters produced by a given clustering algorithm including their biological relevance, unfortunately, a given clustering algorithm can perform poorly under one validation measure while outperforming many other algorithms under another validation measure. A manual synthesis of results from multiple validation measures is nearly impossible in practice, especially, when a large number of clustering algorithms are to be compared using several measures. An automated and objective way of reconciling the rankings is needed.
  
  
  RESULTS
  Using a Monte Carlo cross-entropy algorithm, we successfully combine the ranks of a set of clustering algorithms under consideration via a weighted aggregation that optimizes a distance criterion. The proposed weighted rank aggregation allows for a far more objective and automated assessment of clustering results than a simple visual inspection. We illustrate our procedure using one simulated as well as three real gene expression data sets from various platforms where we rank a total of eleven clustering algorithms using a combined examination of 10 different validation measures. The aggregate rankings were found for a given number of clusters k and also for an entire range of k.
  
  
  BACKGROUND
  R code for all validation measures and rank aggregation is available from the authors upon request.
  
  
  BACKGROUND
  Supplementary information are available at http://www.somnathdatta.org/Supp/RankCluster/supp.htm.
authors.affiliation: Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY 40202, USA.
authors.forename: Vasyl
authors.initials: V
authors.lastname: Pihur
authors.forename: Susmita
authors.initials: S
authors.lastname: Datta
authors.forename: Somnath
authors.initials: S
authors.lastname: Datta
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D019277:Entropy; D020869:Gene Expression Profiling / Q000379:methods*; D009010:Monte Carlo Method; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods