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Design of biased random walks on a graph with application to collaborative recommendation

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  • Leleux, Pierre
  • Courtain, Sylvain
  • Françoisse, Kevin
  • Saerens, Marco

Abstract

This work investigates a paths-based statistical physics formalism, inspired from the bag-of-paths framework, for the design of random walks on a graph in which the transition probabilities (the policy) are biased in favor of some node features. More precisely, given a weighted directed graph G and a non-negative cost assigned to each edge, the biased random walk is defined as the policy minimizing the expected cost rate along the walks while maintaining a constant relative entropy rate. As for the standard bag-of-paths and the randomized shortest paths frameworks, the model assigns a Gibbs–Boltzmann distribution to the set of infinite walks and allows to recover known results from the literature, derived here from a different perspective. Examples of quantities of interest are the partition function of the system, the cost rate, the optimal transition probabilities, etc. In addition, the same formalism allows the introduction of capacity constraints on the expected node visit rates and an algorithm for computing the optimal policy subject to such capacity constraints is developed. Simulation results indicate that the proposed procedure can be effectively used in order to define a Markov chain driving the walk towards nodes having some specific properties, like seniority, education level or low node degree (hub-avoiding walk). An application relying on this last property is proposed as a tool for improving serendipity in collaborative recommendation, and is tested on the MovieLens data.

Suggested Citation

  • Leleux, Pierre & Courtain, Sylvain & Françoisse, Kevin & Saerens, Marco, 2022. "Design of biased random walks on a graph with application to collaborative recommendation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    • Handle: RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009481
    DOI: 10.1016/j.physa.2021.126752
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    References listed on IDEAS

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    4. Kivimäki, Ilkka & Shimbo, Masashi & Saerens, Marco, 2014. "Developments in the theory of randomized shortest paths with a comparison of graph node distances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 600-616.
    5. LAMBIOTTE, Renaud & DELVENNE, Jean-Charles & BARAHONA, Mauricio, 2014. "Random walks, Markov processes and the multiscale modular organization of complex network," LIDAM Reprints CORE 2660, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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