# Find You: Multi-View-Based Location Inference for Twitter Users
## 3 Proposed Methodology
### Network View  
We construct a social network graph based on the @-mention relationship in users' tweets and create an undirected edge between user \(L\) and user \(F\) if user \(L\) mentions user \(F\) in a tweet, in the same way as [PERSON] et al. [27]. We set up users who are mentioned by more than \(J\) different users as celebrity users. In this work, we use GMM to identify local celebrities and improve model inference by retaining local celebrities in the social relationship network to increase the location correlation between users. GMM is a clustering model that implies that all data points are a mixture of multiple Gaussian distributions and searches for a mixture representation of the multidimensional Gaussian model probability distribution to fit arbitrarily shaped data distributions. GMM also provides soft clustering, i.e., determines the probability that each data point belongs to each cluster, and this method is highly effective for identifying overlapping clusters and clusters with varying shapes and sizes. The process of discovering local celebrities using the Gaussian mixture model is depicted in Equations (1)-(4).  
\[PR=GMM(coord,S,\theta_{m}),\quad V=soft\ max(PR) \tag{1}\] \[U=GMM\_means(V_{m_{i}})\] (2) \[cu_{i}\_ner_{T}=\{e|for\ e\ in\ cu_{i}\_ner;\ if\ haver\sin e(e,U_{e })<T\ \}\] (3) \[pro=\frac{Counter\_\_\max(\ (cu_{i}\_ner_{T})}{len(\ cu_{i}\_ner_{T}) }\ pro\in[0,1] \tag{4}\]  
We define the set of celebrity users as \(celebrities=\{cu_{1},cu_{2},\ldots cu_{n}\}\), the neighbors of celebrity users \(cu_{i}\) with location information are defined as \(cu_{i-}\_ner=\{nr_{1},nr_{2},\ldots nr_{m}\}\), \(coord\in R^{b\times 2}\) are the coordinate points of all celebrity users' neighbors with location information, and \(b\) is the total number of data points. \(S\) represents the number of Gaussian distributions in the Gaussian mixture model. \(\theta_{m}\) is the initialization parameter of the model. First, we calculate the probability matrix \(PR\in R^{b\times S}\) of the user coordinate points in the _coord_ belonging to each Gaussian distribution using the GMM, and then the category corresponding to the maximum value of each row of the probability matrix is used as the category label \(V\in R^{b\times 1}\) of the data points by the softmax function. Afterward, the mean coordinates \(U\in R^{b\times 2}\) of the corresponding Gaussian subdistribution (category) for each data point are then found by the model mean function \(GMM\_means()\). For each user \(e\) of \(cu_{i}\_ner\), the dispersion of the distribution of user \(e\) is measured by calculating the _harvesting  
Figure 1: Technical roadmap of the proposed method in this paper. As shown in the above figure, the nodes starting with \(u\) in the tweet view are user nodes; the rest are word nodes. Black edges are user–word edges, and grey edges are word–word edges. After the hidden layer of GCN, \(R(u)\) and \(R(w)\) represent the user’s tweet embedding and word embedding, respectively.  
(semi-positive vector formula) distance between \(e\) and the mean coordinate \(U_{e}\) of the user's corresponding Gaussian distribution, and the users whose _haversine_ distance is greater than a threshold \(T\) are removed to obtain the set \(cu_{i}\_ner_{T}\). The \(Counter_{-}\_max()\) function is defined to find the maximum number of users belonging to the same cluster in \(cu_{i}\_ner_{T}\), and the function \(len()\) is defined to find the total number of sets. If the value of \(pro\) is greater than the threshold \(p\), then \(cu_{i}\_ner\) is regarded as a local celebrity and retained in the social network. This process allows us to identify and retain local celebrities in the social network, taking into account their influence on location correlation among users.