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Handling skewness and directional tails in model-based clustering

Author

Listed:
  • Cristina Tortora

    (San José State University)

  • Antonio Punzo

    (Università di Catania)

  • Brian C. Franczak

    (MacEwan University)

Abstract

Model-based clustering is a powerful approach used in data analysis to unveil underlying patterns or groups within a data set. However, when applied to clusters that exhibit skewness, heavy tails, or both, the classification of data points becomes more challenging. In this study, we introduce two models considering two component-wise transformations of the observed data within a mixture of multiple scaled contaminated normal (MSCN) distributions. MSCN distributions are designed to enable a different tail behavior in each dimension and directional outlier detection in the direction of the principal components. Using the transformed MSCN distributions as components of a mixture, we obtain model-based clustering techniques that allow for 1) flexible cluster shapes in terms of skewness and kurtosis and 2) component-wise and directional outlier detection. We assess the efficacy of the proposed techniques by comparing them with model-based clustering methods that perform global or component-wise outlier detection using simulated and real data sets. This comparative analysis aims to demonstrate which practical clustering scenarios using the proposed MSCN-based approaches are advantageous.

Suggested Citation

  • Cristina Tortora & Antonio Punzo & Brian C. Franczak, 2025. "Handling skewness and directional tails in model-based clustering," Statistical Papers, Springer, vol. 66(5), pages 1-29, August.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01723-9
    DOI: 10.1007/s00362-025-01723-9
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    References listed on IDEAS

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    1. Hung Tong & Cristina Tortora, 2022. "Model-based clustering and outlier detection with missing data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 5-30, March.
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