Trend detection in social networks using Hawkes processes

We develop in this paper a trend detection algorithm, designed to find trendy topics being disseminated in a social network. We assume that the broadcasts of messages in the social network is governed by a self-exciting point process, namely a Hawkes process, which takes into consideration the real broadcasting times of messages and the interaction between users and topics. We formally define trendiness and derive trend indices for each topic being disseminated in the social network. These indices take into consideration the time between the detection and the message broadcasts, the distance between the real broadcast intensity and the maximum expected broadcast intensity, and the social network topology. The proposed trend detection algorithm is simple and uses stochastic control techniques in order to calculate the trend indices. It is also fast and aggregates all the information of the broadcasts into a simple one-dimensional process, thus reducing its complexity and the quantity of data necessary to the detection.

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