ITE: A Structural Entropy Based Approach for Source Detection

This paper studies the problem of source detection, which is to infer the source node out of an aftermath of a cascade, i.e., the observed infected graph G
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of the network at some time. Prior arts have adopted various statistical quantities such as degree, distance or infection size to reflect the structural centrality of the source. In this paper, we propose a new metric which we call the infected tree entropy (ITE), to utilize richer underlying structural features for source detection. Our idea of ITE is inspired by the conception of structural entropy [1], which demonstrated that the minimization of average bits to encode the network structures with different partitions is the principle for detecting the natural or true structures in real-world networks. Accordingly, our proposed ITE based estimator for the source tries to minimize the coding of network partitions brought by the infected tree rooted at all the potential sources, thus minimizing the structural deviation between the cascades from the potential sources and the actual infection process included in G
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. On polynomially growing geometric trees, with increasing tree heterogeneity, the ITE estimator remarkably yields more reliable detection under only moderate infection sizes. In contrast, for regular expanding trees, we still observe guaranteed detection probability of ITE estimator even with an infinite infection size, thanks to the degree regularity property. We also algorithmically realize the ITE based detection that enjoys linear time complexity via a message-passing scheme, and further extend it to general graphs. Experiments on various network topologies confirm the superiority of ITE to the baselines. For example, ITE returns an accuracy of 75% ranking the source among top 5%, far exceeding 45% of the classic algorithms on scale-free networks.