Detecting Structure-correlated Attributes on Graphs

Do users from Carnegie Mellon University form social communities on Facebook? In this paper, we focus on a task of detecting structure-correlated attributes on a graph. A structure-correlated attribute means that the node set activated by the attribute form a community in the graph. This task is relevant to many applications including identifying structure-correlated attributes in social networks, special events in the urban traffic networks, unusual brain activity in the brain connectivity networks, and viruses in cyber-physical systems. To solve this task, we formulate a statistical hypothesis testing to decide if the given attribute activates a community in a graph with interfering by the Bernoulli noise. We propose two statistics: graph wavelet statistic and graph scan statistic. Both are shown to be efficient and statistically effective to detect activations. The intuition behind the proposed statistics is that we study the interaction between graph structure and the given attribute, that is, we denoise the attribute based on the graph structure and localize the underlying community in the graph. We then test the proposed hypothesis tests on simulated data to validate the effectiveness and robustness of the proposed methods. We further apply the proposed methods to two real-world applications: high air pollution detection and ranking attributes for community detection in a coauthorship network collected from IEEE Xplore. The experimental results show that the proposed graph wavelet statistic and graph scan statistic are effective and efficient.