Community Inference from Graph Signals with Hidden Nodes

Many recent works on inference of graph structure assume that the graph signals are fully observable. For large graphs with thousands or millions of nodes, this entails high complexity on the data collection and processing steps. Here, we study a community inference problem on partially observed (sub-sampled) graph signals which sidesteps topology inference, while revealing the coarse structure of the graph directly. Two variants of the inference task are studied: (i) a blind method that infers the communities that the observable nodes belong to; and (ii) a semi-blind method that infers the communities of all nodes using, in addition, side information about the sub-graph between observable and hidden nodes. These techniques for community inference are shown to be efficient and suitable for large graphs analytically and empirically.