Modeling Trust for Recommender Systems using Similarity Metrics 113 i1←dt s direct trust is considered s EicR Let pck: feP, EcR and E, nE> Forj in P do *i has 10 common ratings with f ←tt Serial graph composition It,,<it. tJJ s Parallel graph composition End For j Return it, as iTrust return the indirect trust Fig. 4. The indirect trust calculation. The choice for exploring the trust graphs up to maximum distance of 2 hops was made mostly for reasons of simplicity since with a third hop the number of required calculations increases significantly without a corresponding substantial gain in accu Assuming that the trust transitivity mechanism of Subjective logic is accurate lough then any error measured via our experiment should be considered as error derived from our Similarity-to-Trust transformation formula. In order to evaluate our modeling approach we needed a suitable dataset of user's scores. We chose a publicly available dataset taken from a real CF system known as MovieLens [211 Movielens is a movie recommendation system based on collaborative filtering abl ished at the University of Minnesota. The available dataset contains 1.000.20 anonymous ratings of approximately 3.900 movies made by 6.040 users who joined he service over the year 2000. For our experiment we used a subset of MovieLens that comprised 130000 ratings which were given by 1000 randomly selected users 5.2 Comparative Results and discussion In our tests, we applied each candidate formula to 10 different data sets and the re sults were averaged. Each 100 user dataset built trust graphs of approximately 5000 First, for each pair of users for which indirect trust is calculable the real and the trust-derived similarity are compared. The results are shown in figure 5. Also inter- esting to see is the measured correlation between the number of common expe riences of i andj and the calculated error. Figure 6. a shows the above result picto- rially including each pair of trusted entitiesFig. 4. The indirect trust calculation. The choice for exploring the trust graphs up to maximum distance of 2 hops was made mostly for reasons of simplicity since with a third hop the number of required calculations increases significantly without a corresponding substantial gain in accu￾racy. Assuming that the trust transitivity mechanism of Subjective logic is accurate enough then any error measured via our experiment should be considered as error derived from our Similarity-to-Trust transformation formula. In order to evaluate our modeling approach we needed a suitable dataset of user’s scores. We chose a publicly available dataset taken from a real CF system known as MovieLens [21]. MovieLens is a movie recommendation system based on collaborative filtering es￾tablished at the University of Minnesota. The available dataset contains 1.000.209 anonymous ratings of approximately 3.900 movies made by 6.040 users who joined the service over the year 2000. For our experiment we used a subset of MovieLens that comprised 130000 ratings which were given by 1000 randomly selected users. 5.2 Comparative Results and Discussion In our tests, we applied each candidate formula to 10 different data sets and the re￾sults were averaged. Each 100 user dataset built trust graphs of approximately 5000 relationships. First, for each pair of users for which indirect trust is calculable the real and the trust-derived similarity are compared. The results are shown in figure 5. Also inter￾esting to see is the measured correlation between the number of common expe￾riences of i and j and the calculated error. Figure 6.a shows the above result picto￾rially including each pair of trusted entities. liji it dt , m , * direct trust is considered * Let Ei R * the set of ratings of i * Let P Ki :  fP , Ef  R and ˆ EE fi t 10 For j in P do * i has 10 common ratings with f * jljl dtt , m , jllijli ttt …m ,,,, * Serial graph composition * jlijiji itit t †m ,,,, * Parallel graph composition * End For j Return i j it , as iTrust * return the indirect trust * Modeling Trust for Recommender Systems using Similarity Metrics 113