A unifying framework of rating users and data items in peer-to-peer and social networks

We propose a unifying family of quadratic cost functions to be used in Peer-toPeer ratings. We show that our approach is general since it captures many of the existing algorithms in the fields of visual layout, collaborative filtering and Peer-to-Peer rating, among them Koren spectral layout algorithm, Katz method, Spatial ranking, Personalized PageRank and Information Centrality. Besides of the theoretical interest in finding common basis of algorithms that where not linked before, we allow a single efficient implementation for computing those various rating methods. We introduce a distributed solver based on the Gaussian Belief Propagation algorithm which is able to efficiently and distributively compute a solution to any single cost function drawn from our family of quadratic cost functions. By implementing our algorithm once, and choosing the computed cost function dynamically on the run we allow a high flexibility in the selection of the rating method deployed in the Peer-to-Peer network. Using simulations over real social network topologies obtained from various sources, including the MSN Messenger social network, we demonstrate the applicability of our approach. We report simulation results using networks of millions of nodes.