## 5 Experimental Evaluation  
We conduct experiments to examine whether the proposed LBSN2 vec and PLBSN2 vec can better model user preferences and user-POI interactions in TPD and TCD tasks, comparing with well-known network embedding methods. Collected Instagram data are used for the experiments (the dataset can be crawled via Instagram API: [[https://www.instagram.com/developer/--due](https://www.instagram.com/developer/--due)]([https://www.instagram.com/developer/--due](https://www.instagram.com/developer/--due)) to the privacy issue established by Instagram, we cannot provide the data for download). The dataset contains check-in records and user-user followings collected in New York City from Jan 2012 to Nov 2015. There are 994,412 user-POI check-ins and 1,048,575 fellowship relations. We randomly select 200 POIs and repeat the random selection up to 50 times for the experiments. We use the first 80% chronological check-ins for training and the remaining 20% for testing. We compare LBSN2 vec and PLBSN2 vec with several well-known network embedding methods: node2 vec [18], LINE [19], and GraphGAN [20]. They all map nodes in a network to embedding vectors. The embedding vectors derived from all these methods are fed into the proposed scoring function for both TPD and TCD tasks. We should notice that the difference between our LBSN2 vec and PLBSN2 vec lies in that the former considers only \(w_{ij}\) as the random walk probability while the latter further imposes the penalized parameters. We choose three common measures in the information retrieval field as the evaluation metrics [30]: (a) Precision@N, (b) Recall@N, and (c) NDCG@N:  
\[ \begin{split} Precision@N=&\frac{\#\{Pred(N)\cap GT(N )\}}{N}\\ Recall@N=&\frac{\#\{Pred(N)\cap GT(200)\}}{N}\\ NDCG@N=&\frac{DCG@N}{IDCG@N}\end{split}  \tag{1}\]  
where \(Pred(N)\) is the top-N predicted ranking, and \(GT(N)\) top-N ground-truth ranking. Furthermore, \(DCG@N=\sum_{i=1}^{N}\frac{rel_{i}}{log_{2}[i+1]}\) and \(IDCG@N=\sum_{i=1}^{N}\frac{N+1-i}{log_{2}(i+1)}\). Precision aims at examining whether a method can accurately rank the ground truth at the top position while Recall is used to quantify whether all of the ground truth can be retrieved in the ranking list. The measures of precision and recall are trade-offs between each other. They must be seen together to understand the effectiveness of a model. As for NDCG, it is to estimate how the predicted ranking is close to the ground-truth ranking, which cannot be captured by Precision and Recall. For all methods, we use the same default parameters listed below if they have the settings: the embedding dimension \(d=100\), the number of walks per node = 10, the walk length \(l=80\), and the neighborhood size \(w=6\). In our PLBSN2 vec methods, we set the return parameter \(\rho=0.8\) and chose the user-POI weighting parameter \(\alpha=0.1\) by default. **Results of TPD. ** We present the results of Precision@N (\(N=5,10,\ldots,50\)) in Figure 2. The results of Precision@10, Recall@10, and NDCG@10 are also shown in Table 2. It can be apparently found that LBSN2 vec and PLBSN2 vec outperform the other embedding methods by varying \(N\). In addition, as \(N\) gets increased, PLBSN2 vec is able to stably have the higher Precision values. Among the competing methods, we find that GraphGAN has the worst performance, as it cannot capture the contagion between users and POIs. We think our methods lead to better performance because two key factors are considered. One is the modeling of user-user contagion, and the other is user-POI visiting preference. Such two factors can be better modeled into the embedding vectors of our proposed LBSN2 vec and PLBSN2 vec. **Results of TCD. ** In TCD, we believe the promotion initiator would care more about whether all potential customers can be found. Hence, we report Recall@N in this part. Figure 3 shows the results in Recall@N by varying \(N\). We can see the Recall values with different embedding methods.