114 G. Pitsilis et al parison of all examined alternative formulas Formula Parameter Prediction Error (% Fig. 5. Comparison of the alternative formulas. Due to space limitations we present only the last candidate formula we tested (Type 2 of table 1)and which appears to give the best results(lowest error)com- pared to all other candidates. As can be seen from figure 6. a there is a stochastic re- lationship between the error of the transformation formula applied on pairs of users and the number of common scores of those users. it can also be seen that the maxi- mum error observed is just above 35% as opposed to our first(Existing)approach which produced max error 70%. In terms of average error the new formula is better than twice as good. Another interesting, and obvious, observation from the figure is at as the number of common scores increases the error follows the opposite trend Also the deviation of the error decreases as the common scores increase. The im- ortance of this observation is that it may have a practical value since it makes possible to predict how accurately the derived trust will be calculated. Thus, when a recommendation is to be created a decision can be formed about whether or not a particular relationship should be considered in the process of secondary trust calcu lation. Hence, according to some quality criteria that can be applied, such primary trust relationships that have been built upon 'poor data can be disclosed as they do not provide adequate contribution in the secondary trust calculation In figure 6. b we also show the variance of the similarity prediction error which has the practical meaning of how accurately the trust could be approximated using our model. That could have a practical use: for example it might be used as a crite- rion for choosing the right threshold value for the minimum number of common cores. In this way, the expected error can be determined according to some quality of service criteria that need to be met when building a web of trustComparision of all examined alternative formulas 5 7.5 10 12.5 15 17.5 1 (linear) 3 5 7 9 skew ness value k Erro r (% ) Type 4 Type 3 Prediction based Type 1 Type 2 Formula Parameter used Prediction Error (%) Existing approach 13.71 Type 4 k=1, linear 6.27 Type 4 k=3 7.33 Type 4 k=5 9.96 Type 4 k=7 12.96 Type 4 k=9 16.88 Type 3 k=3 8.34 Type 3 k=5 9.48 Type 3 k=7 10.11 Type 3 k=9 10.49 Type 1 - 6.74 Type 2 - 5.96 Fig. 5. Comparison of the alternative formulas. Due to space limitations we present only the last candidate formula we tested (Type 2 of table 1) and which appears to give the best results (lowest error) com￾pared to all other candidates. As can be seen from figure 6.a there is a stochastic re￾lationship between the error of the transformation formula applied on pairs of users and the number of common scores of those users. It can also be seen that the maxi￾mum error observed is just above 35% as opposed to our first (Existing) approach which produced max error 70%. In terms of average error the new formula is better than twice as good. Another interesting, and obvious, observation from the figure is that as the number of common scores increases the error follows the opposite trend. Also, the deviation of the error decreases as the common scores increase. The im￾portance of this observation is that it may have a practical value since it makes it possible to predict how accurately the derived trust will be calculated. Thus, when a recommendation is to be created a decision can be formed about whether or not a particular relationship should be considered in the process of secondary trust calcu￾lation. Hence, according to some quality criteria that can be applied, such primary trust relationships that have been built upon ‘poor’ data can be disclosed as they do not provide adequate contribution in the secondary trust calculation. In figure 6.b we also show the variance of the similarity prediction error which has the practical meaning of how accurately the trust could be approximated using our model. That could have a practical use: for example it might be used as a crite￾rion for choosing the right threshold value for the minimum number of common scores. In this way, the expected error can be determined according to some quality of service criteria that need to be met when building a web of trust. 114 G. Pitsilis et al