Distributed Informative-Sensor Identification via Sparsity-Aware Matrix Decomposition

Covariance matrices that consist of sparse factors arise in settings where the field sensed by a sensor network is formed by localized sources. It is established that the task of identifying source-informative sensors boils down to estimating the support of the sparse covariance factors. To this end, a novel sparsity-aware matrix decomposition framework is developed that can recover the support of the sparse factors of a matrix. Relying on norm-one regularization a centralized formulation is first derived, when sensors are fully connected. Then, the notion of missing covariance entries is employed to develop a distributed sparsity-aware matrix decomposition scheme. The associated minimization problems are solved using computationally efficient coordinate descent iterations combined with matrix deflation mechanisms. A simple scheme is also developed to set appropriately the sparsity-adjusting coefficients. The distributed framework can provably recover the support of the covariance factors when field sources do not overlap, while each subset of sensors sensing a specific source form a connected communication graph. Different from existing approaches, the novel utilization of covariance sparsity allows distributed informative sensor identification, without requiring data model parameters. Numerical tests corroborate that the novel factorization schemes work well even when the sources overlap.