# Weighted Matrix Factorization Recommendation Model Incorporating Social Trust
## 5 Experimental Evaluation
### Impact of Parameters  
This section analyzes the impact of the trust weight \(w_{1}\), similarity weight \(w_{2}\), and the combined weight \(w_{3}\) on the recommendation accuracy of the Trust-WMF model. The structural diagram of the Trust-WMF model (Figure 2) indicates that this paper divides user ratings into four parts. The first part is the predicted ratings calculated based on the social network; the second part is the predicted ratings calculated based on the user's historical ratings; the third part is the predicted ratings derived from the integration of the overlapping portions of the first and second parts; and the fourth part is the user historical ratings. The first three parts together form the predicted ratings, corresponding to \(R_{pred}\) in Equation (11), and the fourth part corresponds to \(R_{orig}\). In the fourth step of the model, it is necessary to combine these four parts of the ratings for weighted matrix factorization; hence, different weights need to be set for them. Since the fourth part represents the original user ratings, which are the most credible and have the least noise data, this part's weight, \(w_{orig}\), is set as \(1\). However, since the predicted ratings based on the social network and user historical ratings are less credible than the original user ratings, theoretically, the trust weight \(w_{1}\) for the first part, the similarity weight \(w_{2}\) for the second part, and the weight \(w_{3}\) for the ratings derived from the integration of the first three parts should be less than \(1\). Their specific optimal values will be determined by experiments in the following sections. Figure 3 shows the impact of the trust weight \(w_{1}\) and the similarity weight \(w_{2}\) on the recommendation accuracy of the Trust-WMF model for different datasets, Epinions and Ciao, when only considering trust relationships (the first part of the data) or similarity relationships (the second part of the data), respectively. As shown in Figure 3, for Epinions, the recommendation accuracy of the Trust-WMF model exhibits a clear trend under different parameter settings. For trust weight, the model's recommendation accuracy increases with an increase in trust weight, reaching its peak when the trust weight is set to \(0.2\). Beyond this point, as the trust weight further increases, the recommendation accuracy begins to decline. The results indicate that for Epinions, a trust weight of \(0.2\) is optimal. Exceeding this value leads to the negative impact of noise data in  
Figure 3: Impact of w1 and w2 weights on model accuracy on Epinions and Ciao. trust relationships outweighing the effective information contained within, while a value below this does not fully leverage the effective information in trust relationships. In contrast, for similarity weight, the recommendation accuracy of the Trust-WMF model peaks at a similarity weight of 0.1 and gradually decreases as the similarity weight is set below or above 0.1. This finding suggests that the optimal similarity weight for achieving the best recommendation accuracy when only considering similarity relationships is significantly lower than the trust weight required when only considering trust relationships, and the accuracy of the recommendation model that considers only trust relationships is superior to the accuracy of the recommendation model that considers only similarity relationships. This indicates that compared to user similarity relationships, user trust relationships contain richer effective information. For Ciao, the recommendation accuracy of the Trust-WMF model shows a trend similar to that observed with Epinions under varying trust and similarity weights. The key difference lies in the optimal trust weight when only considering trust relationships. For Ciao, the optimal trust weight for the Trust-WMF model is 0.15, as opposed to 0.2 for Epinions. As inferred from Table 1, even though the density of social relationships in Epinions is much lower than Ciao, the rating density in Epinions is sparser compared to Ciao.