## 3 Proposed Approach
In Equation (7), \(n\in NNN\) represents user \(n\) as one of the elements in the set of native's nearest neighbour (NNN). \(r_{nx}\) represents the rating of user \(n\) rates on item \(x\). \(\bar{r}_{n}\) is the mean rating of user \(n\). \(sim_{an}\) represents the similarities between target user \(a\) and native user \(n\). In IBCF, the prediction \(\hat{p}_{af}\) and \(\hat{p}_{an}\) are obtained through the weighted sum method (FANA-IBCF). The equations for both predictions in IBCF are as follows:  
\[\hat{p}_{af}=\frac{\sum_{i}^{I_{f}}\left(sim_{i,I_{f}}\times r_{a,I_{f}} \right)}{\sum_{i}^{I_{f}}\left(\left|sim_{i,I_{f}}\right|\right)} \tag{8}\]  
Figure 2: A graph of native users’ check-in activity in a location-based recommender system. \[\hat{\rho}_{an}=\frac{\sum_{i=1}^{I_{n}}(sim_{i,I_{n}}\times r_{a,I_{n}})}{\sum_{ i}^{I_{n}}(|sim_{i,I_{n}}|)} \tag{9}\]  
In Equation (8), \(I_{f}\) represents all similar items among target user \(a\) and friend users \(f\). \(sim_{i,I_{f}}\) represents the similarity between item \(i\) and all the similar items among target user \(a\) and friend users \(f\). \(r_{a,I_{f}}\) is the rating of target user \(a\) on all the similar items among target user \(a\) and friend user \(f\). In Equation (9), \(I_{n}\) represents all the similar items among target user \(a\) and native users \(n\). \(sim_{i,I_{n}}\) represents the similarity between item \(i\) and all the similar items rated by the target user \(a\) and native user \(n\). \(r_{a,I_{n}}\) is the rating of target user \(a\) with that of the native users \(n\). The users' similarities (similarities between the target user and the friend user, \(sim_{aff}\), and similarities between the target user and the native user, \(sim_{an}\)) and items' similarities (similarities between the target item and the friend item, \(sim_{i,I_{f}}\), and similarities between the target item and native item, \(sim_{i,I_{n}}\)) are computed using the Pearson correlation coefficient (PCC) method. The reason the PCC method was chosen in this approach is because it has been proven by [PERSON] et al. [16] that the PCC method is one of the effective methods to form the nearest neighbourhood in k-NN method. The following equations show the calculations of the similarities between the target user and the friend user, \(sim_{aff}\); similarities between the target user and the native user, \(sim_{an}\); similarities between the target item and the friend item, \(sim_{i,I_{f}}\); and similarities between the target item and the native user, \(sim_{i,I_{n}}\) used in the PCC method. \[sim_{aff}=\frac{\sum_{i\in I}(r_{ai}-\bar{r}_{a})\Big{(}r_{fi}-\bar{r}_{f} \Big{)}}{\sqrt{\sum_{i\in I}(r_{ai}-\bar{r}_{a})^{2}}\sqrt{\sum_{i\in I}(r_{ mi}-\bar{r}_{n})^{2}}} \tag{10}\]  
\[sim_{an}=\frac{\sum_{i\in I}(r_{ai}-\bar{r}_{a})(r_{ni}-\bar{r}_{n})}{\sqrt{ \sum_{i\in I}(r_{ai}-\bar{r}_{a})^{2}}\sqrt{\sum_{i\in I}(r_{mi}-\bar{r}_{n}) ^{2}}} \tag{11}\]  
\[sim_{i,I_{f}}=\frac{\sum_{f\in F}\Big{(}r_{f,i}-\bar{r}_{i}\Big{)}\Big{(}r_{ f,I_{f}}-\bar{r}_{I_{f}}\Big{)}}{\sqrt{\sum_{f\in F}\Big{(}r_{f,i}-\bar{r}_{  
In Equation (13), \(n\in N\) represents a single native user \(n\) of a set of native users \(N\). \(r_{n,i}\) represents the rating that the native user \(n\) given on target item \(i\); meanwhile, \(r_{n,I_{n}}\) represents the rating that native user \(n\) given on native item \(I_{n}\). \(r_{i}\) represents the mean rating of target item i. \(r_{I_{n}}\) represents the mean rating of native item \(I_{n}\).