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Finding Outliers in Gaussian Model-based Clustering

Author

Listed:
  • Katharine M. Clark

    (McMaster University)

  • Paul D. McNicholas

    (McMaster University)

Abstract

Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier inclusion, outlier trimming, and post hoc outlier identification methods, with the former two often requiring pre-specification of the number of outliers. The fact that sample squared Mahalanobis distance is beta-distributed is used to derive an approximate distribution for the log-likelihoods of subset finite Gaussian mixture models. An algorithm is then proposed that removes the least plausible points according to the subset log-likelihoods, which are deemed outliers, until the subset log-likelihoods adhere to the reference distribution. This results in a trimming method, called OCLUST, that inherently estimates the number of outliers.

Suggested Citation

  • Katharine M. Clark & Paul D. McNicholas, 2024. "Finding Outliers in Gaussian Model-based Clustering," Journal of Classification, Springer;The Classification Society, vol. 41(2), pages 313-337, July.
    • Handle: RePEc:spr:jclass:v:41:y:2024:i:2:d:10.1007_s00357-024-09473-3
    DOI: 10.1007/s00357-024-09473-3
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    References listed on IDEAS

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    1. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    2. Katie Evans & Tanzy Love & Sally Thurston, 2015. "Outlier Identification in Model-Based Cluster Analysis," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 63-84, April.
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    4. Qiu, Weiliang & Joe, Harry, 2006. "Separation index and partial membership for clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 585-603, February.
    5. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
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