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Gaussian parsimonious clustering models with covariates and a noise component

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  • Keefe Murphy

    (University College Dublin
    University College Dublin)

  • Thomas Brendan Murphy

    (University College Dublin
    University College Dublin)

Abstract

We consider model-based clustering methods for continuous, correlated data that account for external information available in the presence of mixed-type fixed covariates by proposing the MoEClust suite of models. These models allow different subsets of covariates to influence the component weights and/or component densities by modelling the parameters of the mixture as functions of the covariates. A familiar range of constrained eigen-decomposition parameterisations of the component covariance matrices are also accommodated. This paper thus addresses the equivalent aims of including covariates in Gaussian parsimonious clustering models and incorporating parsimonious covariance structures into all special cases of the Gaussian mixture of experts framework. The MoEClust models demonstrate significant improvement from both perspectives in applications to both univariate and multivariate data sets. Novel extensions to include a uniform noise component for capturing outliers and to address initialisation of the EM algorithm, model selection, and the visualisation of results are also proposed.

Suggested Citation

  • Keefe Murphy & Thomas Brendan Murphy, 2020. "Gaussian parsimonious clustering models with covariates and a noise component," 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. 14(2), pages 293-325, June.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:2:d:10.1007_s11634-019-00373-8
    DOI: 10.1007/s11634-019-00373-8
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    Cited by:

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    2. Keefe Murphy & T. Brendan Murphy & Raffaella Piccarreta & I. Claire Gormley, 2021. "Clustering longitudinal life‐course sequences using mixtures of exponential‐distance models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1414-1451, October.
    3. Sangkon Oh & Byungtae Seo, 2023. "Merging Components in Linear Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 25-51, April.
    4. Dexen D. Z. Xi & Charmaine B. Dean & Stephen W. Taylor, 2021. "Modeling the duration and size of wildfires using joint mixture models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(6), September.
    5. Thiago G. Ramires & Luiz R. Nakamura & Ana J. Righetto & Andréa C. Konrath & Carlos A. B. Pereira, 2021. "Incorporating Clustering Techniques into GAMLSS," Stats, MDPI, vol. 4(4), pages 1-15, November.
    6. Kemmawadee Preedalikit & Daniel Fernández & Ivy Liu & Louise McMillan & Marta Nai Ruscone & Roy Costilla, 2024. "Row mixture-based clustering with covariates for ordinal responses," Computational Statistics, Springer, vol. 39(5), pages 2511-2555, July.

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