Popular Event Tracking

Definitions

1. Network Stream: $G=\{G_{1},G_{2},...,G_{T}\}$ is a stream of network structures. Each element $G_{k}$ in the set is a snapshot of the network at time $t_{k}$. $G_{k}=\{V_{k},E_{k}\}$.

2. Document stream: $D=\{D_{1},D_{2},...,D_{T}\}$ is a stream of document collections. $D_{k}$ is a the set of documents published between time $t_{k-1}$ and $t_{k}$. $D_{k}=\{d_{k,1},d_{k,2},...,d_{k,N}\}$. $d_{(}k,i)$ is the text document associated with user i in time $t_{k}$.

3. Topic: Semantically coherent topic $\theta$ is a multinomial distribution of words $\{p(w|\theta )\}$.

4. Event: $\theta ^{E}=\{\theta _{0}^{E},\theta _{1}^{E},...,\theta _{T}^{E}\}$ is a stream of topics. Among these, $\theta _{0}^{E}$ is either specified by users or be discovered by an event detection algorithm.

5. Interest: for each event, at each time point, each user has a certain level of interest in the event which is expressed as $h_{k}(i)$.