Nonparametric decentralized detection and sparse sensor selection via weighted kernel

The kernel-based nonparametric approach proposed by Nguyen, Wainwright, and Jordan is further investigated for decentralized detection. In contrast with the uniform kernel used in the previous work, a weighted kernel is proposed, where weight parameters serve to selectively incorporate sensors' information into the fusion center's decision rule based on quality of sensors' observations. Furthermore, weight parameters also serve as sensor selection parameters with nonzero parameters corresponding to sensors being selected. By introducing the regularization on weight parameters into the risk minimization framework, sensor selection is jointly performed with decision rules for sensors and the fusion center with the resulting optimal decision rule having only sparse nonzero weight parameters. A gradient projection algorithm and a Gauss-Seidel algorithm are developed to solve the risk minimization problem, which is nonconvex, and both algorithms are shown to converge to critical points. Conditions on the sample complexity to guarantee asymptotically small estimation error are characterized based on analysis of Rademacher complexity. Connection between the probability of error and the risk function is also studied. Numerical results are provided to demonstrate the advantages and properties of the proposed approach based on weighted kernel.