# Find You: Multi-View-Based Location Inference for Twitter Users
## 3 Proposed Methodology
### Multi-View Fusion  
For each node in the tweet view \(tw\) in Figure 1, GCN is used to aggregate its neighboring nodes and its features, and the feature vector representation of the user's tweets is obtained by extracting the embedding of the GCN hidden layer. In this work, we take \(X_{tw}=I_{(m+nw)\times(m+tw)}\) as the initial feature matrix of the nodes in the tweet view (where \(nu\) and \(nw\) are the numbers of users and words, respectively, in the corpus), and the adjacency matrix \(\mathcal{A}_{tw}\) of the tweet heterogeneity graph is the input to the GCN. Using a two-layer GCN with activation functions of ReLU and softmax, the overall forward-propagation process in the tweet view is shown in Equation (10):  
\[Z=f(X_{tw},A_{tw})=\text{softmax}\Big{(}\hat{A}_{tw}\,\text{Re}\,LU\Big{(} \hat{A}_{tw}X_{tw}W_{tw}{}^{(0)}+b_{tw}{}^{0}\Big{)}W_{tw}{}^{(1)}+b_{tw}{}^{ 1}\Big{)} \tag{10}\]  
After one round of training, a cross-entropy loss function is used to calculate the loss of all tagged user nodes. For the tweet feature extraction model in tweet view \(tw\), the user tweet embedding \(R(u)\) in the model's hidden layer is extracted and used as the initial text feature in Figure 1's multi-view \(hyb\). For social networks, access to information about a user's neighbors three hops away can improve location inference [12]. Therefore, three GCN layers are utilized for multi-view fusion to combine the characteristics of tweets and social relationship networks. As input to the multi-view, the initial text features are \(X_{hy}=R(u)\) and the filtered neighborhood matrix \(A_{hy}\) of the social relationship network. Equation (11) depicts the global forward-propagation equation for the multi-view; the activation function uses softmax and Tanh.  
\[Y=f(X_{hy},A_{hy})=\text{softmax}\Big{(}\hat{A}_{hy}\,\text{Tanh}\Big{(}\hat {A}_{hy}\,\text{Tanh}\Big{(}\hat{A}_{hy}X_{hy}W_{hy}{}^{(0)}+b_{hy}{}^{0} \Big{)}W_{hy}^{(1)}+b^{1}\Big{)}W_{hy}^{(2)}+b_{hy}{}^{2}\Big{)} \tag{11}\]  
As the number of layers in the GCN increases, the number of neighborhood members per node grows exponentially. This may lead to the propagation of noisy information from the extended neighborhood members to the user. To address this situation, with the help of ideas from [PERSON] et al. [33], a hierarchical gate is added to the information propagation process at each layer of Equation (11), which in turn controls how much neighborhood information needs to be passed to the nodes. The output of each layer of the modified multilayer graph convolutional network Gate-GCN is shown in Equations (12) and (13):  
\[T\Big{(}H^{l}\Big{)}=\text{Sigmoid}\Big{(}W_{g}^{l}H^{l}+b_{g}^{l}\Big{)} \tag{12}\]  
\[H^{l+1}=H^{l+1}\circ T\Big{(}H^{l}\Big{)}+H^{l}\circ\Big{(}1-T\Big{(}H^{l} \Big{)}\Big{)} \tag{13}\]  
where \(H^{l}\) is the input to layer \(l+1\), and \(W_{g}^{l}\) and \(b_{g}^{l}\) are the gating weights matrix and deviations, respectively. Sigmoid is the activation function; \(\circ\) represents the element multiplication. Finally, based on the vector representation of the obtained user nodes, the softmax function is used to infer the location labels to which they belong, and the cross-entropy loss function is used to calculate the loss.