Modeling Trust for Recommender Systems using Similarity Metrics 111 5 Evaluation When carrying out this experiment we faced the challenge of how to evaluate every alternative formula and what measures to use for comparing the accuracy of our modeling approach. Therefore, we developed and applied the following plan 5.1 The plan Since the goal was to test the accuracy of each candidate formula we considered as he best scenario comparing a known and accepted value of similarity against one that is derived by applying our trust derivation mechanism. More specifically, for each pair of users, lets call them A and B, we first calculated how similar they are, applying Pearsons CC formula over the common experiences of A and B, and then we calculated the indirect trust between them. Next. this trust value was converte to a similarity metric using our formula and, finally, the derived value was com- pared against the original similarity we calculated first. The latter similarity is de- rived from the resulting indirect trust between A and B when subjective logic rules are applied to the graph built by the trust relationships that exist between A and B (see figure 2. )In order to accomplish this, the primary trust between every pair of s0)))) tween A and B, and S'AB the similarity that is derived from the indirect trust of A for B. In the evaluation we compare these two values and we calculate the mean er- ig. 2.. The evaluation diagram. TA.c and TA. D are two of the direct trust values that are used for calculating the in- direct(or secondary) trust of A for B Due to the fact that pearson 's coefficient has unstable behavior when there is a low number of common experiences between two parties, we considered as similar eighbors those who have at least 10 common experiences and we choose to per- form the evaluation test on these pairs of entities as Pearsons similarity is calcula-5 Evaluation When carrying out this experiment we faced the challenge of how to evaluate every alternative formula and what measures to use for comparing the accuracy of our modeling approach. Therefore, we developed and applied the following plan. 5.1 The plan Since the goal was to test the accuracy of each candidate formula we considered as the best scenario comparing a known and accepted value of similarity against one that is derived by applying our trust derivation mechanism. More specifically, for each pair of users, lets call them A and B, we first calculated how similar they are, applying Pearson’s CC formula over the common experiences of A and B, and then we calculated the indirect trust between them. Next, this trust value was converted to a similarity metric using our formula and, finally, the derived value was com￾pared against the original similarity we calculated first. The latter similarity is de￾rived from the resulting indirect trust between A and B when subjective logic rules are applied to the graph built by the trust relationships that exist between A and B. (see figure 2.) In order to accomplish this, the primary trust between every pair of users has to be built pro-actively when making up the trust graph. Figure 2 is a pictorial representation of the entities involved in the evaluation scheme. We call SA,B the similarity that is derived from the common experiences be￾tween A and B, and S’A,B the similarity that is derived from the indirect trust of A for B. In the evaluation we compare these two values and we calculate the mean er￾ror. Fig. 2. .The evaluation diagram. TA,C and TA,D are two of the direct trust values that are used for calculating the in￾direct (or secondary) trust of A for B. Due to the fact that Pearson’s coefficient has unstable behavior when there is a low number of common experiences between two parties, we considered as similar neighbors those who have at least 10 common experiences and we choose to per￾form the evaluation test on these pairs of entities as Pearson’s similarity is calcula￾ble. TA,B A B S’A,B TA,C TC,B C SA,B D E TA,D Modeling Trust for Recommender Systems using Similarity Metrics 111