## 5 Experiments
### Experiment of the I-NMF Model  
In this part, firstly, we test the performance of I-NMF and compare it with CIDAE and O-NeuMF-p on the ML-100K dataset and the ML-1M dataset. Then, we analyze the influence of the parameter of I-NMF on the experimental results on both datasets. Finally, we compare I-NMF with current advanced recommendation algorithms on both datasets. The experimental results prove that our I-NMF model performs better. In addition, we also count the running time of I-NMF and comparison algorithms. Table 4 shows that the performance of I-NMF is better than CIDAE and O-NeuMF-p on both datasets. On the one hand, the imputation ability of CIDAE can alleviate the sparseness of the original data. On the other hand, O-NeuMF-p uses the learning ability of deep neural networks to learn the interaction between users and items. Moreover, both CIDAE and O-NeuMF-p have a good robustness. It can be seen from the experimental results that CIDAE and O-NeuMF-p can complement each other to achieve a higher accuracy. Additionally, it is worth discussing that although CIDAE performs better on the ML-100K dataset, O-NeuMF-p performs better on the ML-1M dataset. This confirms the advantage of the powerful learning ability of deep neural networks for large datasets. In addition, this paper provides a new fusion idea; not only the combination of CIDAE and O-NeuMF-p, but also the combination of different types of recommendation algorithms. Figure 5: Performance of \(r\) based on NDCG@10. We also analyze the effect of the hyper-parameter \(\beta\) controlling the fusion ratio on the accuracy of I-NMF. When \(\beta=0\), CIDAE is used for recommendation alone. Conversely, when \(\beta=1\), O-NeuMF-p is used for recommendation alone. Figure 5(a) shows that when \(\beta=0.6\), I-NMF achieves the highest accuracy on the ML-100K dataset. At this time, I-NMF is better than CIDAE and O-NeuMF-p. Figure 5(b) shows that when \(\beta=0.8\), I-NMF achieves the highest accuracy on the ML-1M dataset. It is worth emphasizing that for all values of \(\beta\), I-NMF is better than CIDAE and O-NeuMF-p on the ML-1M dataset. This also confirms that CIDAE and O-NeuMF-p can complement each other very well. Finally, we compare I-NMF with current advanced recommendation algorithms on both datasets. Table 5 shows that the performance of I-NMF is best on both datasets. On the ML-100K dataset, compared to the state-of-the-art method of ExpoMF, on average, I-NMF obtains 6.8%, 6.9%, and 9.1% relative improvements in HR, NDCG, and MAP metrics, respectively. On the ML-1M dataset, compared to the state-of-the-art method of ExpoMF, on average, I-NMF obtains 5.4%, 5.3%, and 6.0% relative improvements in HR, NDCG, and MAP metrics, respectively. These prove that the accuracy of our I-NMF model is very high. In addition, we also count the running time (a fold cross-validation process) of I-NMF and comparison algorithms in Table 6. It is worth noting that our experiment is run under the CPU (Processor Intel Core i7-6700k, Memory 16 GB), and if it can use the GPU to run, it may be faster. Some parameters of our I-NMF model can affect the running time, such as: \(N_{i}\) (Number of iterations) and \(d\) (Number of hidden nodes) in CIDAE, the number of layers of MLP in O-NeuMF-p, and so on. But the hyper-parameters \(\beta\) (controlling the fusion ratio), \(r\) (controlling the range of random numbers), and \(\alpha\) (the loss weight of the imputed data), and so on, do not affect the runtime. The training time in our model is relatively large. However, during prediction, the running time is negligible, where it only takes 18.2 s for the ML-100K dataset and 2 min for the ML-1M dataset. In addition to this, we can optimize the training time in the future. Figure 6: Performance of \(\beta\) based on NDCG@10.