Entropy-based randomisation of rating networks

Abstract

In the last 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 have different weights due to the score assigned to items. 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 randomisation of (bipartite) rating networks by extending the Configuration Model framework: the randomised 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 non-trivial features of the real network better than other null models. Then, using it as a benchmark, we project the information contained in the real system on one of the layers, showing, for instance, the division in communities of music albums due to the taste of customers, or, in movies due the audience.

arXiv comment12 pages, 30 figures

References in corpus (20)

• Emergence of scaling in random networks
• Fast unfolding of communities in large networks
• Community detection in graphs
• Dynamical and correlation properties of the Internet
• Large-scale topological and dynamical properties of Internet
• The statistical mechanics of networks
• The Dynamics of Protest Recruitment through an Online Network
• Statistically validated networks in bipartite complex systems
• Analytical maximum-likelihood method to detect patterns in real networks
• A fitness model for the Italian Interbank Money Market
• A General Optimization Technique for High Quality Community Detection in Complex Networks
• Maximum likelihood: extracting unbiased information from complex networks
• Efficiently inferring community structure in bipartite networks
• Randomizing bipartite networks: the case of the World Trade Web
• Inferring monopartite projections of bipartite networks: an entropy-based approach
• Enhanced reconstruction of weighted networks from strengths and degrees
• Statistically validated network of portfolio overlaps and systemic risk
• Reconstructing the world trade multiplex: the role of intensive and extensive biases
• Grand canonical validation of the bipartite International Trade Network
• Entropy-based approach to missing-links prediction

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