Tracking Triadic Cardinality Distributions for Burst Detection in Social Activity Streams

In everyday life, we often observe unusually frequent interactions among people before or during important events, e.g., we receive/send more greetings from/to our friends on Christmas Day, than usual. We also observe that some videos suddenly go viral through people's sharing in online social networks (OSNs). Do these seemingly different phenomena share a common structure? All these phenomena are associated with sudden surges of user activities in networks, which we call "bursts" in this work. We find that the emergence of a burst is accompanied with the formation of triangles in networks. This finding motivates us to propose a new method to detect bursts in OSNs. We first introduce a new measure, "triadic cardinality distribution", corresponding to the fractions of nodes with different numbers of triangles, i.e., triadic cardinalities, within a network. We demonstrate that this distribution changes when a burst occurs, and is naturally immunized against spamming social-bot attacks. Hence, by tracking triadic cardinality distributions, we can reliably detect bursts in OSNs. To avoid handling massive activity data generated by OSN users, we design an efficient sample-estimate solution to estimate the triadic cardinality distribution from sampled data. Extensive experiments conducted on real data demonstrate the usefulness of this triadic cardinality distribution and the effectiveness of our sample-estimate solution

Tracking Influential Nodes in Time-Decaying Dynamic Interaction Networks

Identifying influential nodes that can jointly trigger the maximum influence spread in networks is a fundamental problem in many applications such as viral marketing, online advertising, and disease control. Most existing studies assume that social influence is static and they fail to capture the dynamics of influence in reality. In this work, we address the dynamic influence challenge by designing efficient streaming methods that can identify influential nodes from highly dynamic node interaction streams. We first propose a general time-decaying dynamic interaction network (TDN) model to model node interaction streams with the ability to smoothly discard outdated data. Based on the TDN model, we design three algorithms, i.e., SieveADN, BasicReduction, and HistApprox. SieveADN identifies influential nodes from a special kind of TDNs with efficiency. BasicReduction uses SieveADN as a basic building block to identify influential nodes from general TDNs. HistApprox significantly improves the efficiency of BasicReduction. More importantly, we theoretically show that all three algorithms enjoy constant factor approximation guarantees. Experiments conducted on various real interaction datasets demonstrate that our approach finds near-optimal solutions with speed at least $5$ to $15$ times faster than baseline methods.Comment: 14 pages, 15 figure