@article{francoissekivimakietal2017bag-of-path,
title = "A bag-of-paths framework for network data analysis",
journal = "Neural Networks",
volume = "90",
pages = "90 - 111",
year = "2017",
month="6",
issn = "0893-6080",
doi = "10.1016/j.neunet.2017.03.010",
arxiv={1302.6766},
hal={hal-01583972},
url = "http://www.sciencedirect.com/science/article/pii/S0893608017300667",
author = "Fran\c{c}oisse, Kevin and Kivim{\"a}ki, Ilkka and Mantrach, Amin and Rossi, Fabrice and Saerens, Marco",
keywords = {Network science,Link analysis,Distance and similarity on a graph,Resistance distance,
Commute-time distance,Semi-supervised classification},
abstract = "This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representation that considers all paths independently. We show that, under this distribution, the probability of drawing a path connecting two nodes can easily be computed in closed form by simple matrix inversion. This probability captures a notion of relatedness, or more precisely accessibility, between nodes of the graph: two nodes are considered as highly related when they are connected by many, preferably low-cost, paths. As an application, two families of distances between nodes are derived from the BoP probabilities. Interestingly, the second distance family interpolates between the shortest-path distance and the commute-cost distance. In addition, it extends the Bellman-Ford formula for computing the shortest-path distance in order to integrate sub-optimal paths (exploration) by simply replacing the minimum operator by the soft minimum operator. Experimental results on semi-supervised classification tasks show that both of the new distance families are competitive with other state-of-the-art approaches. In addition to the distance measures studied in this paper, the bag-of-paths framework enables straightforward computation of many other relevant network measures.",
language={english},
audience={international},
entrysubtype={article-international-committee},
}