# Improved Recommendations Based on Trust Relationships in Social Networks
## 5 Experiment and Analysis
### Results and Analysis  
We conducted our experiments in three ways. First we performed the experiment towards the users with adequate user-item rating information. Meanwhile, since the main purpose of using trust relationships is to improve the quality of recommendations by solving the problems of cold start and sparsity, we also successively performed the experiments under the conditions of only cold start users and sparse data. In the first experiment, we selected 1526 users and their rating values from Epinions dataset, of which 80% of records are assigned into the training set, and the remaining 20% are distributed into the test set. Since the initial trust degrees in the trust relationships are the same, we decided to train them for certain times, namely, training times to enrich their features. It was also concluded that the character of each trust relationship will be increasingly clear and independent with the growth of the number of training times. Figure 2 presents an RMSE for different methods at varying training times on all users. From Figure 2, we can see that, when the number of training times is not bigger than 20, compared with NCut and TrustWalkerList, IRATR has no absolute advantage in accuracy. This is because NCut is essentially a traditional collaborative filtering method calculating the similarity of user/service with sufficient rating information, but TrustWalkerList and IRATR both need to deal with the trust between users, during which trust relationships are not clear. Along with the increase of training times, TrustWalkerList and IRATR perform better than NCut. When the number of training times is over 20, IRATR has the best accuracy owing to the gradually improved trust relationships. That is, IRATR can improve the accuracy of service recommendations by combining trust degree and user similarity. Consequently, the performance of the proposed IRATR precedes other algorithms on all users under the condition that user-item rating information is sufficient. According to [21], users that provided from 1 to 4 ratings can be identified as cold start users, which in the Epinions dataset are in fact more than 50%. Therefore, we conducted the second experiment by repeating the content in the first one on cold start users to verify the ability of the three methods to solve cold start problems, and the experimental results are shown in Figure 3.  
Figure 3 shows that, compared to other algorithms, IRATR always has a lower error for cold start. In the experiment, NCut performed the worst. This is because few mutual items are rated by cold start users, which means that the similarities of most users or items cannot be accurately calculated in NCut. In contrast, TrustWalkerList can make recommendations without mutual-rated items by employing trust relationships, so its accuracy was a significant improvement. Compared with the  
Figure 3: Comparison on cold start users. Figure 2: Comparison on all users. other two algorithms, IRATR is obviously superior in accuracy. When the number of training times is not less than 30, the accuracy of IRATR is respectively improved by 28.5% and 8.6% on average compared to NCut and TrustWalkerList. IRATR has the lowest RMSE because it can choose more relevant trust users along with trust paths, rather than randomly select neighbors, and enhances the relevance of recommendations from trusted users. In order to test the ability of the three algorithms dealing with sparsity, we in turn set 20%, 40%, 60%, and 80% of the rating data as the test data in the third experiment to compare their RMSEs in different circumstances, and the experimental results are shown in Figure 4.  
It can be seen from Figure 4 that, with the increase in the proportion of the training set in the entire data set, the recommendation effect of these algorithms constantly improved. Among them, the accuracy of IRATR was always the best.