## 3 Methodology
### User Preference Model Construction  
(1) Construct the preference of user on category. Each POI has its latitude and longitude, and each POI can belong to a category. For example, a POI belongs to the restaurant, gym, park, entertainment and so on. We can first construct the category feature vector of POI \(l\) denoted as \(V_{l}^{c}=(f_{l,c1},f_{l,c2},...,f_{l,c1})\). Where \(f_{l,c1}=1\), if POI \(l\) belongs to \(c1\), and \(f_{l,c1}=0\), otherwise. As shown in Table 1, each user has its own preference, and he will visit different POIs. Furthermore, in order to obtain the user's preference for categories from the user's access records to POIs, a computation method similar to TF-IDF is present to calculate the user's preference for the category. TF-IDF (term frequency inverse document frequency [25]) is to evaluate the importance of a word to a document, which is commonly used in the domain of information retrieval and text mining. The importance of a word increases withthe frequency of its appearance in the document, but decreases with the frequency of its appearance in the corpus. The TF-IDF is shown in Equation (1). \[TF-IDF=\frac{f(t_{i},d_{j})}{\sum_{m=1}^{k}f(t_{m},d_{j})}\times log\frac{n}{n(t_ {i})} \tag{1}\]  
where \(f(t_{i},d_{j})\) denotes the frequency of word \(t_{i}\) in document \(d_{j}\), and \(n\) represents the number of documents. In particular, by considering a location category as a word, and considering a user's check-in behavior as a document. Similar to TF-IDF formula above, the formula for the degree of preference of user \(u\) to the category feature \(c\) is shown in Equation (2), it is to estimate the importance of a location category to a user. \[p_{u,c}=\frac{\sum_{k=1}^{m}r_{u,k}\times f_{l_{k},c}}{\sum_{k=1}^{m}r_{u,l_{k} }}\times log\frac{\sum_{k=1}^{m}\sum_{i=1}^{c}f_{l_{k},c_{i}}}{\sum_{k=1}^{m}f _{l_{k},c}} \tag{2}\]  
where \(r_{u,l_{k}}\) denotes the visiting frequency of user \(u\) for location \(l_{k}\) in check-ins. \(f_{l_{k},c_{i}}\) is the category feature model for POI \(l\). \(\sum_{k=1}^{m}r_{u,l_{k}}\times f_{l_{k},c}\) indicates the frequency of user \(u\) visiting the locations belonging to category \(c\) in its check-ins. \(C\) denotes the category of locations. Here \(IDF\) is expressed as the ration of total number of all categories in all locations to the number of location belonging to category \(c\). A location can belong to more than one category. Then the category feature model of user can be represented by Equation (3), and \(p_{u,c}\) is the preference value of user on category \(c\). \[M_{u}^{c}=(p_{u,c_{1}},p_{u,c_{2}},...,p_{u,c_{i}}) \tag{3}\]  
(2) Construct the preference of user on time. As seen from Table 1, it is to be observed that the user has different activities at different times. Time factor plays an important role in analyzing users' preferences. The locations visited by users in different time slices of the day are also very different. For example, some users like to go to gym at night, but some users like to go to the gym at noon. Moreover, users' POI preferences on weekday are also different from those on weekend. On this basis, in order to construct the user's time preference model, time of a day is divided into periodic time slots (e.g., by hour), what is more, we divided the time of day into four parts \(\{T_{1},T_{2},T_{3},T_{4}\}\). \(T_{1}\) denotes 7-12 h for morning, \(T_{2}\) denotes 13-18 h for afternoon, \(T_{3}\) denotes 19-24 h for evening, and \(T_{4}\) denotes 1-6 h. In order to fully reflect the concept of week by time, we have added \(T_{5}\) to represent whether the day is weekend or not. \(T_{5}=1\) if it is weekend, \(T_{5}=0\), otherwise. Thus, the preference model of user \(u_{j}\) for different time period is constructed as shown in Equation (4). \[M_{u}^{T}=(p_{u,t_{1}},p_{u,t_{2}},p_{u,t_{3}},p_{u,t_{4}},p_{u,t_{5}}) \tag{4}\]  
where \(p_{u,t_{k}}=\frac{n_{u,t_{k}}}{\sum_{k=1}^{k}n_{u,t_{k}}}\).