Second-Order Measures of Quality for Binary Classification: A Critical Overview and their Use for Nonlinear Receiver Design - Archive ouverte HAL Access content directly
Journal Articles International Journal of Smart Engineering System Design Year : 2003

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

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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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hal-02362138 , version 1 (13-11-2019)

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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, 2003, 5 (4), pp.401-408. ⟨10.1080/10255810390243700⟩. ⟨hal-02362138⟩
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