Modeling the evolution of item rating networks using time-domain preferential attachment

E. LAVIA; A. CHERNOMORETZ; J. M. BULDU; M. ZANIN; P. BALENZUELA

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2012 vol. 22 p. 1250180 - 1250192

0218-1274

The understanding of the structure and dynamics of the intricate network of connections among people that consumes products through Internet appears as an extremely useful asset in order to study emergent properties related to social behavior.This knowledge could be useful, for example, to improve the performance of personal recommendation algorithms. In this contribution we analyzed five-years records of movie-rating transactions provided by Netflix, a movie rental platform where users rate movies from an on-line catalog. This dataset can be studied as a bipartite user-item network whose structure evolves in time. Even though several topological properties from subsets of this bipartite network have been reported with a model that combinesrandom and preferential attachment mechanisms, there are still many aspects worth to be explored, as they are connected to relevant  phenomena underlying the evolution of the network. In this work, we test the hypothesis that bursty human behavior is essential in order to describe how a bipartite user-item network evolves in time. To that end, we propose a novel model that combines, for user nodes, a network growing prescription based on a preferential attachment mechanism acting not only in the {em topological domain} (i.e. based on node degrees) but also in {em time domain}. In the case of items, the model mixes degree preferential attachment and random selection. With these ingredients the model is not only able to reproduce the asymptotic degree distribution, but also showing an excellent agreement with the Netflix data in severaltime-dependent topological properties.