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<p>Matrix-valued data appears frequently across scientific domains, from satellite imagery to multivariate time series. Yet conventional clustering methods often stumble when confronted with two pervasive real-world challenges: asymmetry in the underlying distributions and the presence of outlying observations. We address these limitations by developing a matrix-variate skew contaminated normal distribution that simultaneously accommodates both heavy-tailed behavior and directional skewness. Our contribution extends beyond simply proposing a new distribution and investigating its fundamental properties. We also embed it within a finite mixture framework. We implement a computationally efficient estimation procedure through an EM-type algorithm. The efficiency of the proposed approach emerges through analyses of simulated scenarios and two substantive applications: multispectral satellite imagery classification and movie rating patterns across demographic groups. Results demonstrate that explicitly modeling both asymmetry and contamination yields superior clustering performance compared to existing alternatives, particularly as data quality degrades.</p>

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A Matrix-Variate Skew Contaminated Normal Distribution with Applications to Model-Based Clustering

  • 期刊论文

  • 发表日期：

    2026年6月21日

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  • Abbas Mahdavi,
  • Anthony F. Desmond,
  • Ahad Jamalizadeh

摘要

Matrix-valued data appears frequently across scientific domains, from satellite imagery to multivariate time series. Yet conventional clustering methods often stumble when confronted with two pervasive real-world challenges: asymmetry in the underlying distributions and the presence of outlying observations. We address these limitations by developing a matrix-variate skew contaminated normal distribution that simultaneously accommodates both heavy-tailed behavior and directional skewness. Our contribution extends beyond simply proposing a new distribution and investigating its fundamental properties. We also embed it within a finite mixture framework. We implement a computationally efficient estimation procedure through an EM-type algorithm. The efficiency of the proposed approach emerges through analyses of simulated scenarios and two substantive applications: multispectral satellite imagery classification and movie rating patterns across demographic groups. Results demonstrate that explicitly modeling both asymmetry and contamination yields superior clustering performance compared to existing alternatives, particularly as data quality degrades.