Parsimonious Ultrametric Manly Mixture Models

Alexa A. Sochaniwsky; Paul D. McNicholas

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arXiv · 2512.13473

Parsimonious Ultrametric Manly Mixture Models

Alexa A. Sochaniwsky·Paul D. McNicholas

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Abstract

A family of parsimonious ultrametric mixture models with the Manly transformation is developed for clustering high-dimensional data where the clusters may be asymmetric. While advances in Gaussian mixture modeling sufficiently handle high-dimensional data, they often struggle with the common presence of cluster skewness. To address this, we incorporate the extended ultrametric covariance structure and the Manly transformation, resulting in the parsimonious ultrametric Manly mixture model family. The ultrametric covariance structure reduces the number of free parameters while identifying latent groups of variables within a nested hierarchy. This phenomenon enables the visualization of hierarchical relationships within clusters, improving cluster interpretability. Additionally, as with many classes of mixture models, model selection remains a fundamental challenge; to this end, a two-step model selection procedure is proposed herein. Through simulation studies and real data analyses, we demonstrate improved model selection via the proposed two-step method, as well as the effective clustering performance.

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Alexa A. Sochaniwsky, Paul D. McNicholas. 2025-12-15. Parsimonious Ultrametric Manly Mixture Models. https://arxiv.org/abs/2512.13473

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