## 5 Experiments
### Experiment of the CIDAE Model  
In this part, firstly, we compare the CIDAE model with the DAE algorithm and the AE algorithm on the ML-100K dataset and the ML-1M dataset. Then, we analyze the influence of parameters of CIDAE on experimental results using the ML-100K dataset.  
Table 2 shows that the performance of the CIDAE model is better than the DAE algorithm and the AE algorithm on both datasets. Additionally, it can be found in Table 2 that CIDAE performs better on the ML-1M dataset. Compared with the AE algorithm, the advantage of CIDAE is that it can alleviate the problem of data sparsity by using the idea of imputation. Compared with the DAE algorithm, CIDAE does not add noise randomly, but performs regular continuous imputation on the output data. Therefore, the recommended ranking of CIDAE achieves a higher accuracy and better quality.  
We also analyze the influence of parameters of CIDAE on experimental results on the ML-100K dataset. The specific parameters are as follows:  
1. \(f(x)\): Imputation function;
2. \(k\): Hyper-parameter in imputation function \(f(x)\);
3. \(N_{i}\): Number of iterations;
4. \(d\): Number of hidden nodes;
5. \(\alpha\): The loss weight of the imputed data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Datasets** & **Models** & **HR05** & **HR010** & **HR0515** & **NDCG@5** & **NDCG@10** & **NDCG@15** & **MAP5** & **MAP@10** & **MAP@15** \\ \hline \multirow{4}{*}{**ML-100K**} & **CIDAE** & **0.421306** & **0.355360** & **0.314747** & **0.447365** & **0.392567** & **0.356907** & **0.339666** & **0.255331** & **0.210620** \\  & DAE & 0.381883 & 0.326142 & 0.291214 & 0.402781 & 0.356766 & 0.326358 & 0.297374 & 0.223106 & 0.184123 \\  & AE & 0.386891 & 0.327394 & 0.292639 & 0.409233 & 0.360020 & 0.239232 & 0.300240 & 0.230385 & 0.183858 \\  & CID/AE-AE & 0.08952 & 0.085419 & 0.075549 & 0.093179 & 0.090405 & 0.083765 & 0.131361 & 0.144688 & 0.145561 \\  & CIDAE-SD & 0.007510 & 0.004360 & 0.003198 & 0.008413 & 0.005948 & 0.004636 & 0.006023 & 0.002972 & 0.002202 \\ \hline \multirow{4}{*}{**ML-1M**} & **CIDAE** & **0.402267** & **0.344528** & **0.309183** & **0.423420** & **0.375963** & **0.345131** & **0.322861** & **0.247092** & **0.206846** \\  & DAE & 0.348828 & 0.304988 & 0.276929 & 0.36341 & 0.328476 & 0.3043959 & 0.269107 & 0.207003 & 0.174379 \\  & AE & 0.350492 & 0.304143 & 0.275353 & 0.368488 & 0.330032 & 0.304874 & 0.270459 & 0.205960 & 0.172438 \\  & CIDAE-VAE & 0.147721 & 0.132783 & 0.122857 & 0.149075 & 0.139169 & 0.132046 & 0.193753 & 0.199708 & 0.199540 \\  & CIDAE-SD & 0.001563 & 0.001495 & 0.001195 & 0.001480 & 0.001417 & 0.001243 & 0.001452 & 0.001454 & 0.001150 \\ \hline \end{tabular}
\end{table}
Table 2: Performance comparison of CIDAE, DAE, and AE based on HRRN, NDCG@N, and MAP@N. (N = 5, 10, 15).  
Figure 4 uses NDCG@10 as an indicator to show the performance of various parameters on CIDAE in the ML-100K dataset. Specifically, Figure 4a shows that different imputation functions \(f(x)\) have different experimental results, but the difference is not obvious. So, we finally chose \(f(x)=kx\) because its form is relatively simple. Conversely, the value of \(k\) can significantly affect the experimental results and we finally chose \(f(x)=1.4x\) because it works best. Figure 4b shows that when the number of iterations is 400, the accuracy of CIDAE is converged. Figure 4c shows that CIDAE achieves the highest accuracy when the number of hidden nodes is 200. So, we finally chose \(N_{i}=400\) and \(d=200\). Figure 4d shows that when \(\alpha=0.1\), CIDAE shows the highest accuracy. In addition, we can see that the accuracy is the worst when \(\alpha=1\). This confirms that it is meaningful to calculate the loss of the imputed data separately with the weight \(\alpha\).