The Network Nullspace Property for Compressed Sensing of Big Data over Networks

We adapt the nullspace property of compressed sensing for sparse vectors to semi-supervised learning of labels for network-structured datasets. In particular, we derive a sufficient condition, which we term the network nullspace property, for convex optimization methods to accurately learn labels which form smooth graph signals. The network nullspace property involves both the network topology and the sampling strategy and can be used to guide the design of efficient sampling strategies, i.e., the selection of those data points whose labels provide the most information for the learning task.