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Model selection for minimum-diameter partitioning.

Michael J Brusco1, Douglas Steinley

  • 1Florida State University, Tallahassee, Florida, USA.

The British Journal of Mathematical and Statistical Psychology
|November 7, 2013
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Summary
This summary is machine-generated.

This study introduces a new algorithm to improve the minimum-diameter partitioning problem (MDPP) by finding all optimal partitions, enhancing cluster analysis and model selection in psychology.

Keywords:
cluster analysiscomplete-linkageminimum-diameter partitioningmodel selection

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Area of Science:

  • * Data Science
  • * Psychology
  • * Cluster Analysis

Background:

  • * The minimum-diameter partitioning problem (MDPP) aims to create compact clusters using partition diameter as a key metric.
  • * Complete-linkage hierarchical clustering is a common heuristic for MDPP but suffers from input sensitivity, suboptimal solutions, and multiple optimal partitions.
  • * These limitations complicate model selection in cluster analysis.

Purpose of the Study:

  • * To address the limitations of complete-linkage hierarchical clustering for the MDPP.
  • * To propose an algorithm that identifies all minimum-diameter partitions for varying numbers of clusters (K).
  • * To facilitate model selection by evaluating partition diameter reduction, number of optima, and partition agreement.

Main Methods:

  • * Development and application of an algorithm to find all minimum-diameter partitions.
  • * Evaluation of the algorithm's performance across five empirical examples from psychological research.
  • * Analysis of partition diameter, number of alternative optima, and partition agreement for model selection.

Main Results:

  • * The proposed algorithm effectively addresses the shortcomings of traditional methods for the MDPP.
  • * It provides a comprehensive set of optimal partitions for different values of K.
  • * Model selection is demonstrably facilitated by considering the range of optimal partitions.

Conclusions:

  • * The proposed method enhances the reliability and interpretability of cluster analysis for the MDPP.
  • * It offers a practical approach for researchers to select optimal cluster solutions in psychological studies.
  • * This facilitates more robust data-driven insights through improved cluster analysis.