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Linear components of quadratic classifiers

Author

Listed:
  • José R. Berrendero

    (Universidad Autónoma de Madrid)

  • Javier Cárcamo

    (Universidad Autónoma de Madrid)

Abstract

We obtain a decomposition of any quadratic classifier in terms of products of hyperplanes. These hyperplanes can be viewed as relevant linear components of the quadratic rule (with respect to the underlying classification problem). As an application, we introduce the associated multidirectional classifier; a piecewise linear classification rule induced by the approximating products. Such a classifier is useful to determine linear combinations of the predictor variables with ability to discriminate. We also show that this classifier can be used as a tool to reduce the dimension of the data and helps identify the most important variables to classify new elements. Finally, we illustrate with a real data set the use of these linear components to construct oblique classification trees.

Suggested Citation

  • José R. Berrendero & Javier Cárcamo, 2019. "Linear components of quadratic classifiers," 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. 13(2), pages 347-377, June.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:2:d:10.1007_s11634-018-0321-6
    DOI: 10.1007/s11634-018-0321-6
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    References listed on IDEAS

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    1. Hanwen Huang & Yufeng Liu & J. S. Marron, 2012. "Bidirectional discrimination with application to data visualization," Biometrika, Biometrika Trust, vol. 99(4), pages 851-864.
    2. Kuhn, Max, 2008. "Building Predictive Models in R Using the caret Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i05).
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