## 4 Experiment and Analysis
### Experimental Results and Analysis  
Initially, the parameters required for the improved CVAE are selected. Figures 6 and 7 illustrate the curve of RMSE results for different epochs (training iterations) during the training process in MovieLens-100K and MovieLens-1M datasets.  
Where epoch stands for the number of iterations, it is observed that as the number of epochs increases, the RMSE of the improved CVAE gradually decreases. The optimal performance is achieved when the epoch reaches 180 in MovieLens-100K. However, 140 achieves the optimum in MovieLens-1M. Therefore, the optimal number of epochs for the improved CVAE model is determined to be 180 and 140.  
From Figures 8 and 10, implicit factors represent the dimensions of the matrix factorization, it can be inferred that as the number of implicit factors increases, the training outcomes stabilize. The optimal points for both RMSE and MAE are found to be 40 in MovieLens-100K. However, it can be seen from Figures 9 and 11 that the optimal point is 15 in MovieLens-1M.  
Then, the RMSE and MAE values of the algorithm were tested under different \(\lambda_{Y}\), \(\lambda_{V,}\) and \(\lambda_{W}\). \(\lambda_{Y}\), \(\lambda_{V}\), \(\lambda_{W}\) represent the regularization parameters of CPMF.  
Figures 12-15 show that the RMSE and MAE curves gradually decrease as \(\lambda\) increases and reach the optimal value after reaching 10 in both datasets. Thus, it is determined that the optimal values of \(\lambda_{Y}\), \(\lambda_{V}\), and \(\lambda_{W}\) are all 10, which indicates the best experimental performance.  
Figure 11: MAE values for different numbers of implicit factors in MovieLens-1M.  
Figure 10: MAE values for different numbers of implicit factors in MovieLens-100K.  
Lastly, to demonstrate the effectiveness of the proposed model in this study, four comparative algorithms are selected for evaluation: the Probabilistic Matrix Factorization (PMF) model proposed by [PERSON] et al. (2016), Collaborative Deep Learning (CDL) recommended by [PERSON] et al. (2018), the Hybrid Deep Probabilistic Model (PHD) introduced by [PERSON] et al. (2019), and the Collaborative Topic Regression (CTR) model combining PMF proposed by [PERSON] et al. (2020). These algorithms are compared against the proposed model using the MovieLens-100K and MovieLens-1M datasets. The experimental results are presented in Figures 16-19. Several experiments were performed and the average value was taken as the final result of RMSE and MAE, as shown in Tables 2 and 3.  
Figure 14: MAE values for different values of \(\lambda\) in MovieLens-100K.  
Figure 13: RMSE values for different values of \(\lambda\) in MovieLens-1M.  
Figure 15: MAE values for different values of \(\lambda\) in MovieLens-1M.  
Figure 16: RMSE values of each algorithm in different epochs in MovieLens-100K.  
Figure 17: RMSE values of each algorithm in different epochs in MovieLens-1M.  
Figure 18: MAE values of each algorithm in different epochs in MovieLens-100K.  
It is evident that in MovieLens-100K, the proposed model in this study reaches convergence at an epoch of 20. Compared to CDL, CTR, PHD, and PMF, the proposed model achieves reductions of 2.26%, 3.30%, 2.57%, and 5.12% in RMSE, respectively. Additionally, the proposed model achieves reductions of 2.63%, 3.66%, 2.53%, and 5.33% in MAE, respectively. In MovieLens-1M, the proposed model reaches convergence at 30 iterations. Compared with CDL, CTR, PHD, and PMF, the RMSE of the proposed model is reduced by 4.39%, 5.49%, 4.22%, and 5.99%, respectively. MAE decreased by 3.28%, 4.17%, 3.08%, and 5.97%, respectively. The final convergence results for RMSE and MAE indicate that the proposed model outperforms other algorithms significantly.  
Experimental results show that compared with the selected algorithms, the proposed model has significant improvement in RMSE and MAE values, which can effectively improve the recommendation performance.