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Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering

In various scientific fields, researchers make use of partitioning methods (e.g., K -means) to disclose the structural mechanisms underlying object by variable data. In some instances, however, a grouping of objects into clusters that are allowed to overlap (i.e., assigning objects to multiple clust...

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Published in:Journal of classification 2022-07, Vol.39 (2), p.264-301
Main Authors: Rossbroich, Julian, Durieux, Jeffrey, Wilderjans, Tom F.
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description In various scientific fields, researchers make use of partitioning methods (e.g., K -means) to disclose the structural mechanisms underlying object by variable data. In some instances, however, a grouping of objects into clusters that are allowed to overlap (i.e., assigning objects to multiple clusters) might lead to a better representation of the underlying clustering structure. To obtain an overlapping object clustering from object by variable data, Mirkin’s ADditive PROfile CLUStering (ADPROCLUS) model may be used. A major challenge when performing ADPROCLUS is to determine the optimal number of overlapping clusters underlying the data, which pertains to a model selection problem. Up to now, however, this problem has not been systematically investigated and almost no guidelines can be found in the literature regarding appropriate model selection strategies for ADPROCLUS. Therefore, in this paper, several existing model selection strategies for K -means (a.o., CHull, the Caliński-Harabasz, Krzanowski-Lai, Average Silhouette Width and Dunn Index and information-theoretic measures like AIC and BIC) and two cross-validation based strategies are tailored towards an ADPROCLUS context and are compared to each other in an extensive simulation study. The results demonstrate that CHull outperforms all other model selection strategies and this especially when the negative log-likelihood, which is associated with a minimal stochastic extension of ADPROCLUS, is used as (mis)fit measure. The analysis of a post hoc AIC-based model selection strategy revealed that better performance may be obtained when a different—more appropriate—definition of model complexity for ADPROCLUS is used.
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subjects Bioinformatics
Clustering
Information theory
Marketing
Mathematics and Statistics
Pattern Recognition
Psychometrics
Signal,Image and Speech Processing
Statistical Theory and Methods
Statistics
title Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering
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