Lin et al KDD 2011

PET：A Statistical Model for Popular Events Tracking in Social Communities

Problem: In this paper, the authors address a method to observe and track the popular events or topics that evolve over time in the communities. Existing methods separate topics and netword structures apart. In this paper, textual topics and network are combined together which makes more sense.

Method: The authors address the event tracking by first defining a term - Popular Event Tracking (PET) in online communities which includes the popularity of events over time, the burstiness of user interest, information diffusion through the network structure and the evolution of topics.

PET leverages a Gibbs Random Field to model the interest of users, depending on their historical status as well as the influence form their social connections. The intuition here is that my current interest will be strongly related with my previous interest. Also my interest will be influenced by my friends which are my connections in social media.

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 $h_{k}(i)$.

Event Tracking Model:

The model in this paper relies on the following three important observations: 1. Interest & Connection: user i's current interest is influenced by i's connections and a stronger tie brings a larger impact. 2. Interest & History: interest values are generally consistent over time. 3. Content & Interest: if user i has a higher level of interest in an event, the content he generates should be more likely to be related to the event.

General Model: First, the authors introduce two reasonable independent assumptions: 1. Given the current network structure and the previous interest status, the current interest status is independent of the document collection. This is a cause-effect assumption that people generate the document at this moment as a result of current interest rather than a cause of current interest.

2. Given the current interest status and the document, the current topic model is independent of the network structure and previous interest status. The reason is that once the user has a certain level of interest toward some event, the contents he produces will only depends on the event and the interest level.

Based on the above assumptions, the inference target becomes: Failed to parse (syntax error): {\displaystyle P(H_k,\theta_k|G_k,D_k,H_{k-1})= P(H_k|G_k,H_{k-1})\dot}