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Second-Order Measures of Quality for Binary Classification: A Critical Overview and their Use for Nonlinear Receiver Design

Abstract : When deriving a detector, we are often led to consider design criteria such as second-order measures of quality. The aim of this paper is to provide a critical overview of these criteria. We first consider the case of deriving unconstrained detectors. We show that second-order criteria must satisfy a non-trivial condition to yield Bayes-optimal receivers, to be considered as relevant criteria for detector design. Next, we address the case where constraints are imposed on the detection structure, leading us to consider some set of admissible detectors. In these conditions we prove that even if there exists a monotonic function of the likelihood ratio in obtaining this statistic via the optimization of a second-order criterion, relevant or not, is not guaranteed. Results are illustrated by simulation examples. Finally, in order to derive nonlinear discriminants via optimization of second-order criteria, we propose a method based on the kernel trick used in the implementation of the well-known support vector machine method. The new method is tested on a number of real data sets.
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https://hal-utt.archives-ouvertes.fr/hal-02362138
Contributor : Jean-Baptiste Vu Van <>
Submitted on : Wednesday, November 13, 2019 - 5:29:46 PM
Last modification on : Thursday, November 14, 2019 - 1:36:43 AM

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Fahed Abdallah, Cédric Richard, Régis Lengellé. Second-Order Measures of Quality for Binary Classification: A Critical Overview and their Use for Nonlinear Receiver Design. International Journal of Smart Engineering System Design, Informa UK (Taylor & Francis), 2003, 5 (4), pp.401-408. ⟨10.1080/10255810390243700⟩. ⟨hal-02362138⟩

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