Modeling Trust for Recommender Systems using Similarity Metrics 115 Statistical results of Error for best Trust Prediction Error for type 2 derivation policy (type 2) HiMno 的四当当数物 Fig 6a(left)and 6. b(right). Graphical presentation of results. e also looked to see if there is any correlation between the error of our trust de- rivation method and the number of common experiences between the two parties and the results show that there is slight correlation when considering linear approx- imation between error and common experiences. More specifically the correlation value declines as the k factor which expresses the skewness(see fig. 1)increases. A more detailed study revealed that the error adapts best to a non-linear approxima- ion. The regression analysis on the results presented in fig. 6. a, and are referred to the type 2 equation showed that the best value of Coefficient of Determination(R) for the above data had a relatively low value of.4135 The increased divergence that is observed for the error as the number of common scores declines can be justified as the result of the noisy behavior of the Correlation Coefficient; therefore the quality of predictions is quite uncertain. Finally, it worth oticing that we observed higher prediction error when the correlation coefficient was between 0 and-1. This can be interpreted as: prediction is easier when users tastes agree and vice versa, or else the proposed formula is not as useful for disa greeing tastes as it is when users agree. This means that using a unique mapping ormula for the whole range of correlation coefficient values is not an ideal solution Otherwise, the first assumption we have made in which, a similarity value of zero would mean that the trustworthiness with the other party should be the half of which corresponds to similarity value l, is not absolutely right 6 Future Work As shown from a more careful examination of the results there is high variation in he error in a way that follows different trends as k changes. For example the error that is measured between a certain pair of nodes i and j does not follow the same trend as that of the average. As also shown in figure 6. b and as discussed in the pre- vious paragraph, the varied deviations in the error need a more detailed analysis of the results to see if it will be possible to justify this observation. For these two it is worth investigating if and how the topological ties of the derived network might be responsible for the variation and if it mig possible to decrease the error even moreCorrelation between the Common Scores and Prediction Error for type 2 0 5 10 15 20 25 30 35 40 45 0 100 200 300 400 500 600 700 Comm on Score s Error in Similarity Prediction Statistical results of Error for best Trust derivation policy (type 2) 0 1 2 3 4 5 6 7 8 000- 050 051- 100 101- 150 151- 200 201- 250 251- 300 301- 350 351- 500 501- 550 551- 600 601- 650 651- 700 Class of common Scores Value (%) Mean Standard Deviation Fig. 6a (left) and 6.b. (right). Graphical presentation of results. We also looked to see if there is any correlation between the error of our trust de￾rivation method and the number of common experiences between the two parties and the results show that there is slight correlation when considering linear approx￾imation between error and common experiences. More specifically the correlation value declines as the k factor which expresses the skewness (see fig.1) increases. A more detailed study revealed that the error adapts best to a non-linear approxima￾tion. The regression analysis on the results presented in fig.6.a. and are referred to the type 2 equation showed that the best value of Coefficient of Determination (R2 ) for the above data had a relatively low value of -0.4135. The increased divergence that is observed for the error as the number of common scores declines can be justified as the result of the noisy behavior of the Correlation Coefficient; therefore the quality of predictions is quite uncertain. Finally, it worth noticing that we observed higher prediction error when the correlation coefficient was between 0 and -1. This can be interpreted as: prediction is easier when users tastes agree and vice versa, or else the proposed formula is not as useful for disa￾greeing tastes as it is when users agree. This means that using a unique mapping formula for the whole range of correlation coefficient values is not an ideal solution. Otherwise, the first assumption we have made in which, a similarity value of zero would mean that the trustworthiness with the other party should be the half of which corresponds to similarity value 1, is not absolutely right. 6 Future Work As shown from a more careful examination of the results, there is high variation in the error in a way that follows different trends as k changes. For example the error that is measured between a certain pair of nodes i and j does not follow the same trend as that of the average. As also shown in figure 6.b and as discussed in the pre￾vious paragraph, the varied deviations in the error need a more detailed analysis of the results to see if it will be possible to justify this observation. For these two reasons it is worth investigating if and how the topological proper￾ties of the derived network might be responsible for the variation and if it might be possible to decrease the error even more. Modeling Trust for Recommender Systems using Similarity Metrics 115