# A bag-of-paths framework for network data analysis

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.
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https://hal.archives-ouvertes.fr/hal-01583972
Contributor : Fabrice Rossi <>
Submitted on : Friday, September 8, 2017 - 10:48:33 AM
Last modification on : Monday, November 27, 2017 - 2:14:02 PM

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Kevin Françoisse, Ilkka Kivimäki, Amin Mantrach, Fabrice Rossi, Marco Saerens. A bag-of-paths framework for network data analysis. Neural Networks, Elsevier, 2017, 90, pp.90 - 111. ⟨10.1016/j.neunet.2017.03.010⟩. ⟨hal-01583972⟩

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