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Benchmarking validity indices for evolutionary K-means clustering performance.

Abiodun M Ikotun1, Faustin Habyarimana1, Absalom E Ezugwu2

  • 1School of Mathematics, Statistics and Computer Science, University of KwaZulu- Natal, KwaZulu-Natal, Pietermaritzburg Campus, Durban, South Africa.

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Summary
This summary is machine-generated.

This study evaluated internal validity indices for Evolutionary K-Means clustering. The Calinski-Harabasz (CH) and Silhouette indices proved most effective for automatic clustering tasks.

Keywords:
Automatic clusteringCluster validity indicesClustering algorithmsEvolutionary k-meansK-meansMetaheuristic optimisation

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Area of Science:

  • Data Science
  • Machine Learning
  • Artificial Intelligence

Background:

  • K-Means clustering requires a predefined number of clusters, limiting its use in automatic data analysis.
  • Evolutionary K-Means (E-KM) algorithms integrate metaheuristics to overcome K-Means limitations, using internal validity indices for automatic cluster determination.
  • The performance of internal validity indices is data-dependent, impacting the reliability of E-KM outcomes.

Purpose of the Study:

  • To evaluate the performance of fifteen internal validity indices within the Enhanced Firefly Algorithm-K-Means (FA-K-Means) framework.
  • To identify the most effective internal validity indices for automatic clustering tasks using an evolutionary approach.
  • To provide practical guidance on selecting fitness functions for E-KM algorithms.

Main Methods:

  • The study employed the Enhanced Firefly Algorithm-K-Means (FA-K-Means) framework, combining Firefly metaheuristics with K-Means.
  • Fifteen distinct internal validity indices were assessed as fitness functions within the FA-K-Means framework.
  • Performance was evaluated across a variety of real-life and synthetic datasets with diverse structural properties.

Main Results:

  • The Calinski-Harabasz (CH) index demonstrated consistently strong performance across various datasets.
  • The Silhouette index also showed robust and reliable performance in determining optimal clustering configurations.
  • Other evaluated indices exhibited variable effectiveness, often dependent on specific dataset characteristics.

Conclusions:

  • The Calinski-Harabasz (CH) and Silhouette indices are recommended for use as fitness functions in Evolutionary K-Means algorithms.
  • These indices offer more reliable and consistent clustering performance for automatic clustering tasks.
  • The findings offer practical insights for researchers and practitioners selecting validity indices in E-KM applications.