Adversarial Link Prediction in Spatial Networks

Social networks arise as a result of complex interactions among people, and homophily plays an important role in this process. If we view homophily as a dominant force in network formation and associate each node with a collection of features, this process gives rise to spatial networks, with likelihood of an edge an increasing function of feature similarity among its incident nodes. A link prediction problem in such spatial networks then amounts to determining whether the pair of nodes are sufficiently close according to this edge likelihood function. We undertake the first algorithmic study of the adversarial side of this problem in which the adversary manipulates features of a subset of nodes on the network to prevent predicting target edges. We show that this problem is NP-hard, even if the edge likelihood function is convex. On the other hand, if this function is convex, we show that the problem can be solved with convex programming when the set of nodes that the adversary needs to manipulate is fixed. Furthermore, if the edge likelihood function is linear, we present approximation algorithms for the case when the features are binary, and we wish to hide only a single edge, and for the case when the features are real-valued but we need to hide an arbitrary collection of edges.