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

Pierre Leleux, Sylvain Courtain, Kevin Françoisse and Marco Saerens

Physica A: Statistical Mechanics and its Applications, 2022, vol. 590, issue C

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.

Keywords: Network data analysis; Biased random walk; Bag-of-paths model; Collaborative recommendation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437121009481
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009481

DOI: 10.1016/j.physa.2021.126752

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().