Covariance and Correlation Kernels on a Graph in the Generalized Bag-of-Paths Formalism

This work derives closed-form expressions computing the expectation of co-presences and of number of co-occurences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two nodes are considered as similar when they appear together on (preferably short) paths of the network. The results are obtained for both regular and hitting paths and serve as a basis for computing new covariance and correlation measures between nodes. Experiments on semi-supervised classification show that the introduced similarity measures provide competitive performances compared to other state-of-the-art distances and similarities.