Sparse sensor selection for nonparametric decentralized detection via L1 regularization

Sensor selection in nonparametric decentralized detection is investigated. Kernel-based minimization framework with a weighted kernel is adopted, where the kernel weight parameters represent sensors´ contributions to decision making. L₁ regularization on weight parameters is introduced into the risk function so that the resulting optimal decision rule contains a sparse vector of nonzero weight parameters. In this way, sensor selection is naturally performed because only sensors corresponding to nonzero weight parameters contribute to decision making. A gradient projection algorithm and a Gauss-Seidel algorithm are developed to jointly perform weight selection (i.e., sensor selection) and optimize decision rules. Both algorithms are shown to converge to critical points for this non-convex optimization problem. Numerical results are provided to demonstrate the advantages and properties of the proposed sensor selection approach.