Multi-objective selection for collecting cluster alternatives

• Published in: Computational statistics Vol. 26; no. 2; pp. 341 - 353
• Main Authors: Kraus, Johann M., Müssel, Christoph, Palm, Günther, Kestler, Hans A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2011; Springer Nature B.V
• Subjects: Algorithms; Categories; Cluster analysis; Clustering; Clusters; Datasets; Economic Theory/Quantitative Economics/Mathematical Methods; Estimating techniques; Leukemia; Machine learning; Mathematical models; Mathematics and Statistics; Optimization; Original Paper; Pareto optimum; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Running; Statistics; Strategy; Studies; Cluster analysis; Cluster validation; Multi-objective optimization; Cluster number estimation
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-011-0244-6

Grouping objects into different categories is a basic means of cognition. In the fields of machine learning and statistics, this subject is addressed by cluster analysis. Yet, it is still controversially discussed how to assess the reliability and quality of clusterings. In particular, it is hard to determine the optimal number of clusters inherent in the underlying data. Running different cluster algorithms and cluster validation methods usually yields different optimal clusterings. In fact, several clusterings with different numbers of clusters are plausible in many situations, as different methods are specialized on diverse structural properties. To account for the possibility of multiple plausible clusterings, we employ a multi-objective approach for collecting cluster alternatives (MOCCA) from a combination of cluster algorithms and validation measures. In an application to artificial data as well as microarray data sets, we demonstrate that exploring a Pareto set of optimal partitions rather than a single solution can identify alternative solutions that are overlooked by conventional clustering strategies. Competitive solutions are hereby ranked following an impartial criterion, while the ultimate judgement is left to the investigator.