Efficient Nonparametric Subgraph Detection Using Tree Shaped Priors

Non-parametric graph scan (NPGS) statistics are used to detect anomalous connected subgraphs on graphs, and have a wide variety of applications, such as disease outbreak detection, road traffic congestion detection, and event detection in social media. In contrast to traditional parametric scan statistics (e. g. , the Kulldorff statistic), NPGS statistics are free of distributional assumptions and can be applied to heterogeneous graph data. In this paper, we make a number of contributions to the computational study of NPGS statistics. First, we present a novel reformulation of the problem as a sequence of Budget Price-Collecting Steiner Tree (B- PCST) sub-problems. Second, we show that this reformulated problem is NP-hard for a large class of nonparametric statistic functions. Third, we further develop efficient exact and approximate algorithms for a special category of graphs in which the anomalous subgraphs can be reformulated in a fixed tree topology. Finally, using extensive experiments we demonstrate the performance of our proposed algorithms in two real-world application domains (water pollution detection in water sensor networks and spatial event detection in social media networks) and contrast against state-of-theart connected subgraph detection methods.

Authors

• Nannan Wu Tianjin University
• Feng Chen
• Jianxin Li Beihang University
• Baojian Zhou Fudan University
• Naren Ramakrishnan Virginia Tech

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