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This paper investigates a real-world application of the free energy distance between nodes of a graph [14, 20] by proposing an improved extension of the existing Fraud Detection System named APATE [36]. It relies on a new way of computing the free energy distance based on paths of increasing length, and scaling on large, sparse, graphs. This new approach is assessed on a real-world large-scale e-commerce payment transactions dataset obtained from a major Belgian credit card issuer. Our results show that the free-energy based approach reduces the computation time by one half while maintaining state-of-the art performance in term of Precision@100 on fraudulent card prediction.

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This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences 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 often appear together on (preferably short) paths of the network. The different expressions are obtained for both regular and hitting paths and serve as a basis for computing new covariance and correlation measures between nodes, which are valid positive semi-definite kernels on a graph. Experiments on semi-supervised classification problems show that the introduced similarity measures provide competitive results compared to other state-of-the-art distance and similarity measures between nodes.

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