# Information Fusion-Based Deep Neural Attentive Matrix Factorization Recommendation
## 4 Experiments
### Experimental Results and Analysis
#### 4.2.3 Result 3: The Impact of the Number of Hidden Layers on the Performance  
In Section 4.1.2, we generalize the IFDNAMF model to the GMF+MLP model by removing the interaction layer, attention layer, and pooling layer. Through the experiments and analysis in Result 1, it is not difficult to conclude that by adding multi-layer neural network to the GMF model, the model is endowed with the ability that models the high-order interaction between the user and the item, so the model could learn more abstractive features, and then the model obtains a better ability of expression. To explore the influence of the number of hidden layers on the performance of recommendation systems of the model, we set up control group experiments with hidden layers of 1, 2, 3, and 4, respectively.  
Figure 3: The HR@10 and NDCG@10 of models with different potential vector dimension on Books crossing. (**a**) HR@10. (**b**) NDCG@10.  
The model with one layer of neural network is denoted as MLP-1, MLP-2 represents the model with two layers of neural network, etc. We conducted the experiments on MovieLens and Book-crossing and got the HR@10 and NDCG@10 of the four models: GMF+MLP, concat, sum pooling, and IFDNAMF of the four control groups experiments under the optimal potential vector dimension, respectively. The results are shown in Figures 4 and 5.  
Figures 4 and 5 show that as the number of hidden layers increases continuously from 1, the HR@10 and NDCG@10 of the model are constantly growing, and the model's performance gets significantly improved. This is because the single layer neural network can map input data to another abstract space to learn more abstractive features, and by increasing the number of hidden layers, the model could learn richer and more abstractive information to model the interaction between users and items better. In addition, through introducing hidden layers, the model obtains the ability to learn non-linearity, which improves the model's ability of expression. This indicates that by adopting the deep neural network, the IFDNAMF model could learn high-order interaction between users and items, thereby the model's performance of recommendation systems gets improved further. However, as the number of layers of the deep neural network increases further, the HR@10 and NDCG@10 increase slowly, even when the number increases from 3 to 4, the HR@10 and NDCG@10 of the concat model on MovieLens begin to decline, which indicates that it is not that the more layers the MLP has and the deeper the neural network is, the better the model performance of recommendation systems is. This is because too many hidden layers will lead to over-fitting, which will limit the performance of recommendation systems of  
Figure 4: The HR@10 and NDCG@10 of models with different layers on MovieLens. (**a**) HR@10. (**b**) NDCG@10.  
the model. Meanwhile, due to too many hidden layers in the neural network, the model parameters will increase exponentially, which will increase the difficulty to train and make it difficult for model to converge.  
In addition, the HR@10 and NDCG@10 of the models with attribute features, namely the concat model, sum pooling model, and IFDNAMF model, are higher than the GMF+MLP model, which further indicates that the introduction of auxiliary information is beneficial to the performance of the model. Furthermore, it can be seen that the sum pooling model performs better than the concat model, which connects feature vectors through concatenating operation. Further, the IFDNAMF model performs best. This also verifies that it is meaningful to improve the performance of the model by explicitly completing the crossover between feature domains through the element-wise product and assigning different weights to the cross-features through the attention mechanism.