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Adaptive distributed sparsity-aware matrix decomposition

Data covariance matrices that consist of sparse factors arise in settings where the field sensed by a network of sensors is formed by localized sources. It is established that the task of identifying source-informative sensors boils down to estimating the support of the underlying sparse covariance factors. Relying on norm-one regularization a distributed sparsity-aware framework is developed. The associated minimization problems are solved using computationally efficient coordinate descent iterations that are combined with matrix deflation mechanisms. A simple scheme is also developed to set appropriately the sparsity-adjusting coefficients which can provably recover the support of a covariance matrix factor. Adaptive implementations that account for time-varying settings are also considered. The novel utilization of covariance sparsity does not require knowledge of the data model parameters, while numerical tests demonstrate that the novel schemes outperform existing alternatives.