# Combining Post Sentiments and User Participation for Extracting Public Stances from Twitter
## 3 The Proposed Method
### User Influence Estimation  
In addition to determining the sentiment score of post contents, we further consider the user influence on public opinions. Users might have different impacts to other people according to their social relationships. In addition to acquiring users' friend relationship, we can also learn from their interactions with other people. In this paper, we define the _user authority_ in terms of their post-response interactions with other users. Specifically, the linking structures inherent in the interactions are extracted to represent the corresponding relations among users and posts. Then, the social influence of each person can be estimated based on link analysis. After observing the major functions in popular social networking platforms such as Twitter and Facebook, we can find the major types of interactions including: _posting_, _retweeting_ (_forwarding_), _relying_, _like_, and _following_ in different social networking platforms. The assumption is that: if a user posts more articles with more people participating in related discussions, he (or she) will be more influential to the related topics. In this paper, we construct user-post graphs G = {V, E}, where the nodes V include users U and posts P, and the edges E represent various user actions on posts. Since we only consider the interactions between users and posts, there will be no edge between the same types of nodes. It's therefore a bipartite graph. For example, user \(u_{i}\) can post, forward, reply, and like a post \(p_{j}\), which forms an edge \(e_{ij}\). Different types of interactions might have different meanings and thus different influence weights. If we do not distinguish between these types, it becomes an unweighted graph, which can be simply calculated using the idea of PageRank [4] or ObjectRank [31]. In this paper, we assume a different but fixed weight for each type of interactions. Thus, we extend the idea of TURank [11] by considering more types of edges for different user-post relations. In our preliminary experiments, due to the limitation of Twitter API, the real data collected are limited in the amount of _follows, replies,_ and _likes_. Without appropriate amounts of data, we cannot successfully learn these relations for the estimation of influence weights. Thus, in this paper, we only consider the bi-directional user-post interaction graphs as constructed using _posting_ and _forwarding_ relations. Specifically, since the retweeting function in Twitter can be either simply forwarding a message, or commenting on the post, we further distinguish them into two types: _sharing_, and _retweeting_. From the initial observation, an example configuration of edge weights are set as shown in Figure 2.  
As shown in Figure 2, we focus on user-post graphs consisting of three types of user actions: _posting_, _sharing_, and _retweeting_, together with the corresponding reactions on posts: _posted_, _shared_, and _retweeted_. After constructing the user-post graphs, the corresponding influence scores can be calculated based on the idea of PageRank [4], except that the weight \(w(e)\) of an edge \(e\) in the transition matrix is modified as in Equation (3):  
\[w(e)=\frac{w(e_{s})}{outdeg(v,e_{s})} \tag{3}\]  
where edge \(e\) can belong to different type \(e_{s}\) with the corresponding weight \(w(e_{s})\). The \(outdeg(v,e_{s})\) denotes the out-degree of node \(v\) with edges of type \(e_{s}\). In real cases such as Facebook or Twitter, the number of users and posts can easily reach the order of millions or more. Thus, the user-post graph and the corresponding adjacency matrix can be very huge in size. In addition to the storage size required, the computational costs can be tremendous for a typical off-the-shelf personal computer. We propose two solutions. First, we divide the dataset into subsets by dates. Since users usually browse the first few posts without reading them all, we observe that users will only read, share, and like a post within no more than one day.