A simple extension of the bag-of-paths model weighting path lengths by a Poisson distribution

This work extends the bag-of-paths model by introducing a weighting of the length of the paths in the network, provided by a Poisson probability distribution. The main advantage of this approach is that it allows to tune the mean path length parameter which is most relevant for the application at hand. Various quantities of interest, such as the probability of drawing a path from the bag of paths, or the join probability of sampling any path connecting two nodes of interest, can easily be computed in closed form from this model. In this context, a new distance measure between nodes of a network, considering a weighting factor on the length of the paths, is defined. Experiments on semi-supervised classification tasks show that the introduced distance measure provides competitive results compared to other state-of-the-art methods. Moreover, a new interpretation of the logarithmic communicability similarity measure is proposed in terms of the new model