# Weighted Matrix Factorization Recommendation Model Incorporating Social Trust
## 5 Experimental Evaluation
### Comparison of Model Recommendation Performance  
To validate the effectiveness of the Trust-WMF model in recommendation results, Trust-WMF was compared with the following recommendation models:  
* PMF [25]: Probabilistic Matrix Factorization Model: This model considers the latent factors of users and items under a Gaussian distribution in probabilistic matrix factorization; \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Users** & **Items** & **Ratings Density** & **Social Relationships** & **Social Relationship** \\ \hline Epinions & 49,289 & 139,738 & 664,824 & 0.0097\% & 487,183 & 0.0201\% \\ Ciao & 7375 & 105,114 & 284,086 & 0.0366\% & 111,781 & 0.2055\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information about the datasets. * SoRec [11]: It captures the latent features of users and items by jointly decomposing the user-item rating matrix and the user-user social network matrix;
* SoReg [15]: This model uses social information to regularize the user feature vectors;
* SocialMF [14]: It assumes that a user's preference information largely depends on the preference information of their trusted friends, representing the user feature vector as the weighted average of their trusted friends' feature vectors;
* TrustMF [12]: This model originates from the genesis of trust relationships, separately modeling trusting and being trusted behaviors;
* NeuMF [19]: This model combines neural networks with matrix factorization, using neural networks to replace the traditional inner product operation;
* DiffNet++ [21]: Based on graph neural networks, model the high-order social influence diffusion in social networks and interest diffusion in interest networks within a unified model;
* GDSRec [23]: Based on graph neural networks, this model considers attitude biases that might exist among different users as vectors and integrates these biases into the process of learning user and item representation vectors. For the model evaluation, 80% of the data was randomly selected as the training set, and 5-fold cross-validation was conducted. For the Trust-WMF model, the parameter settings were as follows: learning rates \(\gamma_{1}\) = 0.02 and \(\gamma_{2}\) = 0.005 and regularization parameters \(\lambda_{1}\) = 0.005, \(\lambda_{2}\) = 0.5, \(\lambda_{3}\) = 0.005, and \(\lambda_{4}\) = 0.5. Additionally, the number of latent space features was set to 10. Table 2 shows the performance comparison of the Trust-WMF model and the aforementioned models on the Epinions and Ciao datasets. Based on the results in the table, we can see:  
1. Among all models, PMF, which only utilizes user historical ratings, has the lowest accuracy. Meanwhile, the accuracy of SoRec, SoReg, SocialMF, and TrustMF, which integrate user social networks, is higher than PMF. This indicates that incorporating user social networks effectively enhances the accuracy of recommendation models. Distinct from the modeling methods of SoRec, SoReg, and SocialMF, TrustMF considers from the perspective of the generation of trust relationships. It models trust and being trusted behaviors separately, mapping users into trustor feature vectors and trustee feature vectors. This approach enables more effective utilization of the relationships between users in social networks. Although the NeuMF model does not integrate user social networks, its accuracy is still higher than PMF, proving that using neural networks can learn deeper features of users and items, thus improving the accuracy of recommendation models. 2. The experimental results of the SoRec, SoReg, SocialMF, TrustMF, DiffNet++, and GDSRec models show that the accuracy of DiffNet++ and GDSRec is significantly higher than the other four models. All six models utilize user historical ratings and social networks, but DiffNet++ and GDSRec are trained based on graph neural network architecture. This suggests that graph neural networks enhance the precision of recommendation models.