Entropy-based randomization of rating networks

In recent years, due to the great diffusion of e-commerce, online rating platforms quickly became a common tool for purchase recommendations. However, instruments for their analysis did not evolve at the same speed. Indeed, interesting information about users' habits and tastes can be recovered just considering the bipartite network of users and products, in which links represent products' purchases and have different weights due to the score assigned to the item in users' reviews. With respect to other weighted bipartite networks, in these systems we observe a maximum possible weight per link, that limits the variability of the outcomes. In the present article we propose an entropy-based randomization method for this type of networks (i.e., bipartite rating networks) by extending the configuration model framework: the randomized network satisfies the constraints of the degree per rating, i.e., the number of given ratings received by the specified product or assigned by the single user. We first show that such a null model is able to reproduce several nontrivial features of the real network better than other null models. Then, using our model as benchmark, we project the information contained in the real system on one of the layers: To provide an interpretation of the projection obtained, we run the Louvain community detection on the obtained network and discuss the observed division in clusters. We are able to detect groups of music albums due to the consumers' taste or communities of movies due to their audience. Finally, we show that our method is also able to handle the special case of categorical bipartite networks: we consider the bipartite categorical network of scientific journals recognized for the scientific qualification in economics and statistics. In the end, from the outcome of our method, the probability that each user appreciate every product can be easily recovered. Therefore, this information may be employed in future applications to implement a more detailed recommendation system that also takes into account information regarding the topology of the observed network.