Correlated Compressive Sensing for Networked Data

We consider the problem of recovering sparse correlated data on networks. To improve accuracy and reduce costs, it is strongly desirable to take the potentially useful side-information of network structure into consideration. In this paper we present a novel correlated compressive sensing method called CorrCS for networked data. By naturally extending Bayesian compressive sensing, we extract correlations from network topology and encode them into a graphical model as prior. Then we derive posterior inference algorithms for the recovery of jointly sparse and correlated networked data. First, we design algorithms to recover the data based on pairwise correlations between neighboring nodes in the network. Next, we generalize this model through a diffusion process to capture higher-order correlations. Both real-valued and binary data are considered. Our models are extensively tested on several real datasets from social and sensor networks and are shown to outperform baseline compressive sensing models in terms of recovery performance.