title: Clustering ensembles: models of consensus and weak partitions.
abstract: Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets.
authors.affiliation: Nielsen Media Research, 501 Brooker Creek Blvd., Oldsmar, FL 34677, USA. alexander.topchy@nielsenmedia.com
authors.forename: Alexander
authors.initials: A
authors.lastname: Topchy
authors.forename: Anil K
authors.initials: AK
authors.lastname: Jain
authors.forename: William
authors.initials: W
authors.lastname: Punch
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods; D008954:Models, Biological; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity