Modeling Ranking Data in Social Networks

Ranking of items arises in many situations in our daily lives. Very often, not all the items are ranked, resulting in a set of incomplete ranking data. A typical example of incomplete ranking data is movie recommendation where users in a social media platform rated a number of movies and some of these users may be friends of each other. As not all movies are rated by the same user, after converting ratings to rankings, such dataset becomes a set of incomplete rankings with friendship connections among the users in a social network. It is known that individual choice behaviors may be influenced strongly from their peers or friends on social media. So far, traditional ranking models do not account for such spatial or network dependence. This project aims at developing new probabilistic models for ranking data in a social network. As individuals’ rank-order preference behaviors are often correlated with those of their “friends”, it is anticipated that the new models should be able to capture such social network effects and make better inferences, for instance, predicting ranks of the unranked items, inferring the latent social positions, and identifying latent groups. They can help us to have a better understanding of some sociological phenomena such as homophily as well as the social patterns of the individuals and items. First of all, we develop conditional models of ranking data for a given social network by extending the traditional ranking models to incorporate peer effects. Secondly, we will adopt a latent space approach to model both ranking data and social network jointly. Under this approach, individuals and items are represented by points in a latent space, and the distance between two individual points and the distances from an individual point to the item points will then determine the likelihood of a connection between the two individuals and the probability of observing a ranking given by the individual respectively. One can also develop joint models by combining a marginal model for ranking data (social network) and a conditional model of social network (ranking data). Efficient estimation procedures of the new models will be developed. To provide a comprehensive study under various conditions, the proposed models will be applied to analyze a number of real-world datasets and semi-synthetic datasets. It is believed that the new models can provide both practical and theoretical contributions to the analysis of ranking data in a social network.

Funding Source: RGC - General Research Fund (GRF)