Supervised Kemeny Rank Aggregation for Influence Prediction in Networks

Identifying influential individuals in a network is commonly addressed through various socio-metrics like PageRank, Hub and Authority scores [1], etc. These metrics are primarily based on the actor's location in the network [2] and often captures only a subset of the critical factors that are usually at play while predicting influence in networks like, relationship of the network (type of edge), degree of relationship (weight of the edge), etc. As each measure captures some aspect of a user's influence in the network, it may be beneficial to combine them in order to more accurately identify influencers. In this paper, we focus on methods for combining such influence measures. One straightforward way to combine socio-metrics is to aggregate the scores given by each metric to produce an aggregate score for an individual, using methods like Logistic Regression. However, given that the individual influence measures produce an ordering of elements and not just a point-wise score, we can instead leverage approaches of rank aggregation. Methods for rank aggregation have been extensively used in Social Choice Theory, where there is no ground-truth ranking, and as such are unsupervised. In this paper we introduce several supervised approaches to rank aggregation that can be trained on the ground-truth ordering of a subset of elements. We empirically illustrate various advantages of supervised rank aggregation methods through two case studies: (1) social network data from Twitter and (2) citation network data from arXiv.org. Supervised Rank Aggregation: We consider two key rank aggregation techniques, Borda [3] and Kemeny [4]. Borda aggregation is easy to compute but does not satisfy an important goodness property called Extended Condorcet Criteria [4]. Kemeny satisfies this criterion but is NP-hard to compute [4]. So, we use Local Kemenization (LK) [4], which is a relaxation of Kemeny aggregation that still satisfies the Extended Condorcet Criterion. Borda and Kemeny aggregations, being motivated from social choice theory, strive for fairness and hence treat all rankers as equally important. However, fairness is not a desirable property in our setting, since we know that some individual rankers (measures) are likely to perform better than others in our target tasks. In fact, given the ordering of a (small) set of candidates, we can estimate the performance of individual rankers and use this to produce a better ranking on a new set of candidates. In order to accommodate such supervision, we extend Borda and LK aggregation to incorporate weights associated …