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This work derives closed-form expressions computing the expectation ofco-presence and of number of co-occurrences of nodes on paths sampled from anetwork according to general path weights (a bag of paths). The underlying ideais that two nodes are considered as similar when they often appear together on(preferably short) paths of the network. The different expressions are obtainedfor both regular and hitting paths and serve as a basis for computing newcovariance and correlation measures between nodes, which are valid positivesemi-definite kernels on a graph. Experiments on semi-supervised classificationproblems show that the introduced similarity measures provide competitiveresults compared to other state-of-the-art distance and similarity measuresbetween nodes.

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