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Fractionally-Supervised Classification

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  • Irene Vrbik
  • Paul McNicholas

Abstract

Traditionally, there are three species of classification: unsupervised, supervised, and semi-supervised. Supervised and semi-supervised classification differ by whether or not weight is given to unlabelled observations in the classification procedure. In unsupervised classification, or clustering, all observations are unlabeled and hence full weight is given to unlabelled observations. When some observations are unlabelled, it can be very difficult to a priori choose the optimal level of supervision, and the consequences of a sub-optimal choice can be non-trivial. A flexible fractionally-supervised approach to classification is introduced, where any level of supervision—ranging from unsupervised to supervised—can be attained. Our approach uses a weighted likelihood, wherein weights control the relative role that labelled and unlabelled data have in building a classifier. A comparison between our approach and the traditional species is presented using simulated and real data. Gaussian mixture models are used as a vehicle to illustrate our fractionally-supervised classification approach; however, it is broadly applicable and variations on the postulated model can be easily made. Copyright Classification Society of North America 2015

Suggested Citation

  • Irene Vrbik & Paul McNicholas, 2015. "Fractionally-Supervised Classification," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 359-381, October.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:3:p:359-381
    DOI: 10.1007/s00357-015-9188-9
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    References listed on IDEAS

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    1. Andrews, Jeffrey L. & McNicholas, Paul D. & Subedi, Sanjeena, 2011. "Model-based classification via mixtures of multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 520-529, January.
    2. Vrbik, I. & McNicholas, P.D., 2012. "Analytic calculations for the EM algorithm for multivariate skew-t mixture models," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1169-1174.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
    5. Berry, J. Calvin, 1994. "Improving the James-Stein estimator using the Stein variance estimator," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 241-245, June.
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    Citations

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    Cited by:

    1. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    2. Hossein Baloochian & Hamid Reza Ghaffary, 2019. "Multiclass Classification Based on Multi-criteria Decision-making," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 140-151, April.
    3. Sanjeena Subedi & Paul D. McNicholas, 2021. "A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 89-108, April.
    4. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.
    5. Ahfock, Daniel & McLachlan, Geoffrey J., 2023. "Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review," Econometrics and Statistics, Elsevier, vol. 26(C), pages 124-138.
    6. Wei, Yuhong & Tang, Yang & McNicholas, Paul D., 2019. "Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 18-41.
    7. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    8. Sharon M. McNicholas & Paul D. McNicholas & Daniel A. Ashlock, 2021. "An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 264-279, July.
    9. Douglas L. Steinley, 2019. "Editorial: Journal of Classification Vol. 36–2," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 175-176, July.
    10. Michael P. B. Gallaugher & Paul D. McNicholas, 2019. "On Fractionally-Supervised Classification: Weight Selection and Extension to the Multivariate t-Distribution," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 232-265, July.
    11. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    12. Douglas L. Steinley, 2016. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 327-330, October.
    13. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.

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