## 3 Methodology
### POI Group Recommendation Algorithm
The calculation formula is:  
\[f_{g,l}=\frac{\sum_{v\in U}sim_{g,v}\times r_{v,l}}{\sum_{v\in U}sim_{g,v}} \tag{14}\]  
(4) Group recommendation based on intragroup divergence. Each group is composed of multiple users, so the overall preference of a group for POI is mainly determined by the different preferences of each member in the group. With the size of the group increasing, that is to say, the group is of three or more users, there is complex relationship within the group. Users in the group may have different opinions, and have disagreements about a location. Intragroup divergence is the preference difference of all users in the group for a location \(l\). The most common method is to calculate the difference of visiting probability of any two members in the group to location \(l\). To compute the probability of a user in the group \(g\), we calculate the difference of visiting probability of a group \(g\) from the group to location \(l\). The difference of visiting probability of a group \(g\) from the group to location \(l\) is calculated by the similarity between the group and the user \(v\). group for location \(l\), we have introduced the concept that if a friend of user \(u\) has visited location \(l\), then it has a high probability of being recommended to user \(u\). The probability of user \(u\) to location \(l\) can be calculated by the check-ins of \(u^{\prime}\)s friends. Regarding the calculation of the degree of divergence within the group, we use the formula to calculate the divergence relationship between the historical visits of the group. As shown in Equation (15), to compute the degree of divergence of the group \(d_{g,l}\) by considering the relationship between any two members in the group. \[d_{g,l}=\frac{2}{n(n-1)}\times\sum|\delta(u,l)-\delta(u^{{}^{\prime}},l)| \tag{15}\]  
where \(\delta(u,l)-\delta(u^{{}^{\prime}},l)\) represents the divergence of two members for each location. \(\delta(u,l)\) denotes the probability of a user in the group for location \(l\). The calculation formula of \(\delta(u,l)\) is shown in Equation (16). \(n\) denotes the size of group. \[\delta(u,l)=\frac{1}{|A_{u}|}\times\sum_{v\in A_{u}}r(v,l) \tag{16}\]  
The number of friends visited by each user in the group, and \(A_{u}\) is the set of friends of user \(u\) (similar to user \(u\)), where \(r(v,l)\) indicates whether user \(v\) has checked in location \(l\). If so, \(r(v,l)=1\); otherwise, \(r(v,l)=0\). The disagreement of users in the group on location \(l\) is manifested in the differences of users in the group on location \(l\). We believe that the preference of users in the group for location \(l\) can be computed by calculating whether the user's friend collection has visited the location. If the user's friends have visited the location, it means that the user may be willing to visit the location. Therefore, the percentage of friends visiting the location in the friend collection are taken as the user's preference for location \(l\) in the group. Finally, The POI group recommendation result can be obtained based on Equation (17). It combines the similarity and divergence within the group. \(f^{{}^{\prime}}_{g,l}\) denotes a new preference value for a group. The divergence degree of users has a negative impact on the final recommendation score. The top-N POIs with larger values are selected as the recommendation for a group to visit. \[f^{{}^{\prime}}_{g,l}=\alpha f_{g,l}-(1-\alpha)d_{g,l} \tag{17}\]  
In the above equation, \(\alpha\) is a tuning parameter, and the value range is 0 to 1. It is related to group recommendation with different group size.