# Social Recommendation Based on Quantified Trust and User's Primary Preference Space
## 6 Experiments and Validations
### Experimental Results
#### 6.3.2 Experimental Results of the TPSR Framework
In summary, experiments with two main tasks of scoring predictions and recommendation lists for recommended areas indicate that the model of the primary preference space proposed by TPSR in this paper has achieved excellent results in reducing the scoring error and improving the quality of the recommendation list. Experiments on different sparsity users. The experimental results in datasets with different sparsity can reflect the effect of methods to mitigate the sparsity and cold-start problems mentioned in Section 1. In order to verify the prediction ability of different models for users with different sparsity levels, we first divide the four datasets into seven groups according to the number of single-user ratings, so as to observe the degree of cold-start. Instead of calculating the average prediction accuracy of all users, this part of the experiment calculates the prediction accuracy of each user group to measure the _RMSE_ on users with different cold-start levels. The lower the number of users with single-user ratings, the higher the degrees of the cold-start and sparsity problems. Figure 8 shows the number of users as the range of the number of single-user ratings changes, which is used to indicate the sparsity and cold-start degree of the user score in each dataset. In FilmTrust, Epinions and Douban, the number of users in each group varies widely. In FilmTrust, more than 90% of users rated less than 50, and FilmTrust has the problem of data sparse and cold-start. In Epinions, approximately 50% of users rated less than 5, indicating that Epinions has the highest sparsity and cold-start problem. In the Douban, 40% of the user scores are greater than 200, indicating that the sparseness and cold-start are low and the user rating information is relatively sufficient. In Figure 8, the horizontal coordinate of the line graph is the range of the number of single-user ratings, and the ordinate is the RMSE corresponding to the predict the user's ratings. For the experiments on each dataset, users with a lower number of single-user ratings have a poorer prediction accuracy. The higher the number of single-user rating items, the more historical records the user has, and the better the cold-start problem can be alleviated. It can be seen from the prediction results of different methods that the proposed TPSR framework reduces the _RMSE_ in each group. The _RMSE_ of the TPSR, TPMF, TrustPMF and SoRec models on each group is lower than the PMF model (only utilizing the interaction information, without the trust information), which proves that the combination of trust information and rating information can improve the recommendation effect, and TPSR reduces the _RMSE_ more significantly. In the group with a lower number of ratings, especially in the group with the number of single-user ratings between 0 and 5, TPSR is especially effective to reduce of _RMSE_. The results show that TPSR can obviously alleviate the sparsity and cold-start problems. Figure 8: User grouping and grouping experiment results.