# A Discriminative-Based Geometric Deep Learning Model for Cross Domain Recommender Systems
## 4 Experimental Setup and Results Analysis
### Evaluation Scheme and Settings  
Similar to [35, 36], \(P\) items related to each user were randomly chosen to form a training set with the rest used as the test sample for each dataset. To conduct a comparative analysis of the models under both dense and sparse settings, \(P\) was set to 1 and 10 in our experiments, and for each value of \(P\), the process was repeated randomly ten times with different training sets with their average values reported. As has been discussed extensively in [25, 34, 54, 55, 56, 57], recall was utilized as the measure for performance since the rating information implicitly is obtained as feedback [9, 19]. In situations where zero entries are obtained, it suggests that either the users are not aware of the item's existence or are not interested. Moreover, such precision is not appropriate for measuring performance. As in many recommender systems, the predicted ratings of the candidate items are sorted and the top M items are recommended to the target user. As a result, the recall M for each user is then measured as:  
\[\text{Recall}\ =\frac{\text{Number of items that the user likes among the Top M}}{\text{total no of items that the user likes}} \tag{11}\]  
Finally, the average recall value over all users is reported. The cutoff point of the mean average precision (mAP) is also set at 500 for each user.  
In the experiments, the optimal parameters were determined for all the baseline approaches (TCH, TMO, PTUPCDR, CDRIB, DLMF and GDL) using a validation set. The parameter was set to 10 for all the base models. With reference to TCH, TMO, PTUCPDR and CDRIB, the optimal performance of these models is achieved using a two-layer architecture. For DLMF and GDL, the values of a, b and K were set to 1, 0.01 and 50, respectively. A grid search was performed on the parameters with the training dataset split using ten-fold cross validation. For the proposed D-GDL approach, the values of w, a, and b were set to 1, 0.01, and 0.01, respectively, for all experiments. With regards to the Amazon and the Imhonet datasets, 80% of the users were chosen to represent the training set while the remaining 20% used as the test user set with ten-fold user stratified cross-validation settings. The best set of parameters was chosen using 20% of users for validation and 80% as their ratings  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Statistics** & **Movies** & **Books** & **Games** & **Perfumes** \\ \hline Users & 426,897 & 3,622,448 & 72,307 & 19,717 \\ \hline Items & 90,793 & 167,384 & 12,768 & 3640 \\ \hline Density & 0.00073 & 0.00022 & 0.00140 & 0.00350 \\ \hline Number of records & 28,281,946 & 13,438,520 & 1,324,945 & 253,948 \\ \hline Average no. of ratings per user & 66.30 & 37.0771 & 18.2339 & 12.8796 \\ \hline Average no. of ratings per item & 311.4992 & 80.2856 & 103.7708 & 69.7659 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of the Imhonet datasets used.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Statistics** & **Movie** & **Book** \\ \hline Users & 9043 & 38,032 \\ \hline Items & 30,279 & 105,651 \\ \hline Ratings & 1,264,244 & 3,637,313 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistics of the Amazon Datasets Used.  
from the training set. This procedure was repeated 10 times with the average performance of the algorithm reported.