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Geometrical Aspects of Discrimination by Multilayer Perceptrons

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  • Ingrassia, Salvatore

Abstract

We investigate some geometrical aspects of the discriminant functions of the kindfp(x)=[summation operator]pk=1 ck[tau](a'kx) for suitable constantsak, ckwhere[tau]is a sigmoidal transformation. This function is realized by a multilayer perceptron with one hidden layer. These results are applied in the analysis of the discriminating power offp. In particular, we prove that the class of finite populations[Omega]1and[Omega]2that can be distinguished byfpis monotonically increasing inpand we give a minimal sufficientpleading to a complete separation between[Omega]1and[Omega]2.

Suggested Citation

  • Ingrassia, Salvatore, 1999. "Geometrical Aspects of Discrimination by Multilayer Perceptrons," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 226-234, February.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:226-234
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    Cited by:

    1. Isabella Morlini, 2006. "On Multicollinearity and Concurvity in Some Nonlinear Multivariate Models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 3-26, May.

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