## 4 Experiments
### Discussion and Results  
First, we evaluate the influence of the embedding and hidden layer on the performance of MIPR. Figures 4 and 5 illustrate the performance of MIPR using different combinations of embeddings and hidden layers on top-10 recommendations of Foursquare and Gowalla, respectively. Note that, except for the 200-dimensional hidden layer, the performance (i.e., precision) is improved with the increasing dimension of embeddings on the datasets. In addition, the performance is better when the dimension of embeddings is higher than the dimension of hidden layers. In summary, the performance (i.e., precision) is not improved monotonously with the increasing dimension of embeddings or hidden layers. It would be better to select the parameters based on specific scenarios. according to \(loss_{gen}\) (i.e., \(\alpha=0\) and \(\beta=0\)); however, the GAN-based structure is capable of improving the performance if the proposed approach takes \(loss_{pred}\) and \(loss_{loc}\) into account (especially \(loss_{pred}\)). To investigate the convergence of our proposed approach, we conduct an experiment which traces the loss of generator (i.e., the convex linear combination \(J^{G}\) of \(loss_{pred}\), \(loss_{gen}\) and \(loss_{loc}\) shown in Equation (8)) and discriminator, \(J^{D}\), during the process of training each batch (i.e., the batch size is 32) on Foursquare. Figure 7 illustrates that the fluctuation of loss become stable after the 5 th epoch. Although there exists a fluctuation from the 15 th and 18 th epoch, the trend of loss becomes stable again after the 19 th epoch. In summary, the stable trend of loss demonstrates the convergence of the proposed approach. Second, we investigate the effectiveness of geographical influence and adversarial learning to the POI recommendation. Tables 3 and 4 show the performance of MTPR using different components on Foursquare and Gowalla, respectively. The std error of each metric is given in the bracket next to the corresponding metric. The density of the dataset (i.e., actual check-in records of individuals) causes the low values of Precision, Recall, and F1-measure. As we can observe from Table 2, although the check-in records of each user are about 50, most of the users only have 20-30 check-in records where these records also have many duplicate POIs. In summary, MTPR outperforms MTPR-NoGeo and MTPR-NoGen, which means the components of geographical module and adversarial learning are capable of improving the performance of POI recommendations. In detail, MTPR-NoGen outperforms MTPR-NoGeo, which is a model that consists of LSTM but without the consideration of geographical influence, which demonstrates that the geographical influence is more significant than the mechanism of adversarial learning in the current POI recommendation task. In addition to all the variants of MTPR, the precision is decreasing with the increase of TopN recommendations. In other words,  
Figure 6: The performance using different combinations of alpha and beta on Foursquare. Figure 7: The convergence of the proposed approach on Foursquare. the approaches rank the relevant recommendation (i.e., the hitting recommendations based on the testing dataset) at the top of the list, which shows the effectiveness of MTPR. Third, we compare MTPR with the baselines to validate the effectiveness of our proposed approach in the task of TopN recommendations. Table 5 shows the comparison between the generated samples (i.e., recommendations) and the real check-ins. These cases (i.e., POI ids) are sampled from four users where the contextual check-in sequence is ordered by timestamps, the real check-ins are ordered by POI ids, and the Top10 recommendations are ordered by the relevance to the user preferences. The real check-ins are the actual check-in records following the contextual check-in sequence. The first case is familiar in the recommendations where the 896 th POI hits the user preference while the remaining recommendations are invalid.