# Similarity Calculation via Passage-Level Event Connection Graph
## 3 Model Details
### Node Evaluation  
Typically, \"If one author emphases a topic (or a clue), everything in his article is related to this topic (or clue)\" [41; 42]. It is straightforward to make an assumption that the core event in one text should be supported by the other events. If we project all the events mentioned in one text to a plane, the core event will be the point surrounded by the other event. In our paper, we just project events to a plane, while treating the event as a polygon which includes several nodes (i.e., trigger and arguments). Trigger is the key element in the event and decides event type. Thus, we put trigger at the center of the polygon. These two situations ensure that the center of the graph should be the core event. The remaining job becomes how to locate the center of the graph. PageRank, a popular centrality measurement, is chosen to fulfil this task. PageRank is proposed by Google and used to rank web pages in searching engine. The principle behind PageRank is random walk [43]. When one surfer randomly surfs on a graph, the node visited most frequently should be the central node (owning the largest PageRank value). We just follow the traditional PageRank measurement. The only difference is to use the transition matrix (noted as \(A\)) formed from our event connection graph. The size of \(A\) is \(v*v\). \(v\) denotes the number of nodes in the graph. Each entry in \(A\) is the transition probability from one node in the row to another node in the column. For example, given a surfer who travels on the event connection graph, if (\(i\),\(j\)) is an arc, \(A_{ij}\) denotes the transition probability that this surfer visits \(j\) by jumping from \(i\), and can be set as the reciprocal of the out degree of node \(i\). On the opposite, if (\(i\),\(j\)) is not an arc, this probability is 0. Via PageRank, each node in the event connection graph has a value. This value indicates the importance of the node in the graph, which can be utilized to locate the core event. There are two kinds of nodes in the graph, i.e., trigger and argument. If the node of the largest PageRank value is a trigger, we then extract the trigger and the arguments belonging to this trigger as the core event. This way just treats the nodes in the polygon which takes the trigger of the largest value as its center as the core event. Otherwise, if the node of the largest value is an argument, we then output the nodes in all the polygons which take this argument as their intersection node. Figure 3 gives the PageRank values of the nodes in Figure 2. In this figure, the node \"President of USA\" owns the largest value (marked in red color). Since \"President of USA\" is an argument, we output the nodes in the polygons which take \"President of USA\" as their intersection node. The chosen nodes are marked in a yellow color in Figure 3. These nodes just indicate the core event expressed by the previous paragraph with four sentences. However, the chosen event is not accurate, since the main meaning of this paragraph is about the meeting of two leaders in USA and China. Let \(S_{i}\) and \(S_{j}\), respectively, denote the two sets which include the chosen nodes in the event connection graphs formed from the given texts, \(text_{i}\) and \(text_{j}\). To calculate the similarity between \(text_{i}\) and \(text_{j}\), we can form a matrix, noted as \(TS_{ij}\). Each element in this matrix denotes the similarity between two chosen nodes in \(S_{i}\) and \(S_{j}\), respectively. Since the node in the graph is either trigger word or argument word, it can be represented as vector via GloVe [10]. Their similarity can be measured by vector similarity via Cosine. Some triggers or arguments may be phrase (composing of several words). We then average the vectors of the words in that phrase as its vector representation. We take the mean of all the elements in \(TS_{ij}\) as the similarity between \(text_{i}\) and \(text_{j}\).