Modeling User Networks in Recommender Systems

Recommender systems, in the collaborative filtering variation, are popular tools used to drive users out of information clutter, by letting them select ¿interesting¿ items based on the preferences of similarly minded users. In such a system as more users come in to evaluate items (be they information pieces, products or otherwise), a network of users starts to be formed. In this paper we are interested in the dynamics of such a network, in particular we investigate if there is a hidden law that captures the essence of such networks irrespective of their size. The discovery of such a law would allow, among other usages, generation of synthetic data sets, realistic enough to be used for simulation purposes. Furthermore, it would be useful for information-seeking activities such as locating known experts or influential users on a particular subject. Similar work in related fields suggested the existence of power-laws, which seem to be ubiquitous. However, in our work we did not detect the presence of such a law, instead we discovered an exponential relationship between the nodes of a graph representing users, and edges representing similarity between users. In particular the logarithm of the degree of node is linearly related to the ranking of the node in a decreasing order. The above conclusion is justified by extended experiments on two versions of the movie lens data set (one comprised 100,000 user evaluations, while the other comprised 1,000,0000 evaluations).