Private Hierarchical Clustering in Federated Networks

Analyzing structural properties of social networks, such as identifying their clusters or finding their central nodes, has many applications. However, these applications are not supported by federated social networks that allow users to store their social contacts locally on their end devices. In the federated regime, users want access to personalized services while also keeping their social contacts private. In this paper, we take a step towards enabling analytics on federated networks with differential privacy guarantees about protecting the user's social contacts. Specifically, we present the first work to compute hierarchical cluster trees using local differential privacy. Our algorithms for computing them are novel and come with theoretical bounds on the quality of the trees learned. Empirically, our differentially private algorithms learn trees that are of comparable quality (with at most about 10% utility loss) to the trees obtained from the non-private algorithms, while having reasonable privacy (0.5 łeq ε łeq 2). Private hierarchical cluster trees enable new application setups where a service provider can query the community structure around a target user without having their social contacts. We show the utility of such queries by redesigning two state-of-the-art social recommendation algorithms for the federated social network setup. Our recommendation algorithms significantly outperform the baselines that do not use social contacts.