Shannon’s Entropy for Network Optimization
Résumé
This contribution deals with binary detection networks optimization using an entropy-based criterion, from a priori probabilities and conditional PDF. The reduction of communication costs is the key focus of distributed detection networks. On the contrary, their performance is lower compared to centralized networks, because the fusion center does not receive all the available information to make the final decision. The optimization of a parallel distributed network with N sensors leads to a set of 2N + N nonlinear equations, that can only be solved in particular cases, assuming statistical independence of the local observations, and for small-sized networks. In order to reduce the number of equations to solve, Shannon’s entropy is used to select relevant sensors for the decision process. Once the relevant sensors are selected, assuming conditional independence of the observations, we demonstrate that the optimization of an elementary component of detection consists in applying a variable threshold on the likelihood ratio, which depends on a posteriori probabilities. A gradient algorithm is proposed to find this threshold. The optimization results of the elementary component of detection using entropy and Bayes’ criteria are compared : the proposed approach is characterized by an interesting property of robustness with respect to rare events, and with respect to events for which a priori probabilities are uncertain. In particular, the obtained ROC curve does not recede from the ideal point.