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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.
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Evaluating methods for addressing skewness in clustering: a focus on generalized hyperbolic mixture models
In model-based clustering, the population is assumed to be a combination of sub-populations. Typically, each sub-population is modeled by a mixture model component, distributed according to a known probability distribution. Each component is considered a cluster. Two primary approaches have been used in the literature when clusters are skewed: (1) transforming the data within each cluster and applying a mixture of symmetric distributions to the transformed data, and (2) directly modeling each cluster using a skewed distribution. Among skewed distributions, the generalized hyperbolic distribution is notably flexible and includes many other known distributions as special or limiting cases. This paper achieves two goals. First, it extends the flexibility of transformation-based methods as outlined in approach (1) by employing a flexible symmetric generalized hyperbolic distribution to model each transformed cluster. This innovation results in the introduction of two new models, each derived from distinct within-cluster data transformations. Second, the paper benchmarks the approaches listed in (1) and (2) for handling skewness using both simulated and real data. The findings highlight the necessity of both approaches in varying contexts.
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- Award ID(s):
- 2209974
- PAR ID:
- 10621649
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Journal of Statistical Computation and Simulation
- ISSN:
- 0094-9655
- Page Range / eLocation ID:
- 1 to 16
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1080/00949655.2025.2502535
