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Unobserved classes and extra variables in high-dimensional discriminant analysis

Author

Listed:
  • Michael Fop

    (University College Dublin)

  • Pierre-Alexandre Mattei

    (Université Côte d’Azur, Inria, CNRS, Laboratoire J.A. Dieudonné, Maasai team)

  • Charles Bouveyron

    (Université Côte d’Azur, Inria, CNRS, Laboratoire J.A. Dieudonné, Maasai team)

  • Thomas Brendan Murphy

    (Université Côte d’Azur, Inria, CNRS, Laboratoire J.A. Dieudonné, Maasai team)

Abstract

In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a subsequent stage with respect to when the learning sample was collected. In this situation, the classifier built in the learning phase needs to adapt to handle potential unknown classes and the extra dimensions. We introduce a model-based discriminant approach, Dimension-Adaptive Mixture Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt to the increasing dimensionality. Model estimation is carried out via a full inductive approach based on an EM algorithm. The method is then embedded in a more general framework for adaptive variable selection and classification suitable for data of large dimensions. A simulation study and an artificial experiment related to classification of adulterated honey samples are used to validate the ability of the proposed framework to deal with complex situations.

Suggested Citation

  • Michael Fop & Pierre-Alexandre Mattei & Charles Bouveyron & Thomas Brendan Murphy, 2022. "Unobserved classes and extra variables in high-dimensional discriminant analysis," 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. 16(1), pages 55-92, March.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:1:d:10.1007_s11634-021-00474-3
    DOI: 10.1007/s11634-021-00474-3
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    References listed on IDEAS

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