Fig 2 Collaborative Recommending Sy sten 1)(v2)(3)(V4 noted that we do not include the links between Ui->Vi, Vi, since we are modeling a collaborative rating scheme where(assuming that the item being recommended ha not been observed by the active user)the predicted rating will only depend on those ratings given by its neighbors The similarity measure proposed in this paper is a combination of two different, but complementary, criteria: vote correlation between common items and the overlap sim(Ua, Ub)=abs (PCC(Ua, Ub))x D(Ua, Ub) The first criterion, which is normally used as the basis for calculating the weights in different collaborative systems, attempts to capture those similar users, i.e. those with the highest absolute value of pearsons correlation coefficient defined as PCC(Ua, Ub)= (ra. j-Fa)(rb, j-Fb) 7b)2 where the summations overj are over those items for which users Ua and Ub have recorded votes and Ta is the mean vote for user Ua. It should be noted that PCC ranges from +1 to-1: +l means that there is a perfect positive linear relationship between users;-I means that there is a perfect negative linear relationship: a correlation of 0 means that there is no relationship. Therefore, when there are no common items in Ua and Ub voting records, then PCC(Ua, Ub)=0 by default. In our approach, by using the absolute value of PCC, abs (PCC), we consider that both positively(those with similar ratings) and negatively correlated users(those with opposite tastes)might help- to predict an active user's final rating The second criterion tries to penalize those highly correlated neighbors which are based on very few co-rated items, which have proved to be bad predictors(Herlocker et al. 1999). We might therefore take into account the number of items that both a and Ub rated simultaneously, i. e. their overlap degree. In particular, we consider that the quality of Ub as the parent of variable Ua is directly related with the probability of a user Ua rating an item which has been also rated by Ub. This criterion can be defined by the following expression 2 For instance. if whenever Ub rates as like Ua rates with dislike, then knowing that U, had rated item with like provides information about Uas possible ratingUncertainty in group recommending 215 Fig. 2 Collaborative Recommending System Topology U2 V0 V1 V2 V3 V4 V5 U0 U1 U3 U4 U5 noted that we do not include the links between Ui −→ Vi, ∀i, since we are modeling a collaborative rating scheme where (assuming that the item being recommended has not been observed by the active user) the predicted rating will only depend on those ratings given by its neighbors. The similarity measure proposed in this paper is a combination of two different, but complementary, criteria: vote correlation between common items and the overlap degree, i.e. sim(Ua, Ub) = abs(PCC(Ua, Ub)) × D(Ua, Ub) (1) The first criterion, which is normally used as the basis for calculating the weights in different collaborative systems, attempts to capture those similar users, i.e. those with the highest absolute value of Pearson’s correlation coefficient defined as PCC(Ua, Ub) =
j(ra,j − r a)(rb,j − r b)
j(ra,j − r a)2
j(rb,j − r b)2 (2) where the summations over j are over those items for which users Ua and Ub have recorded votes and r a is the mean vote for user Ua. It should be noted that PCC ranges from +1 to −1: +1 means that there is a perfect positive linear relationship between users; −1 means that there is a perfect negative linear relationship; a correlation of 0 means that there is no relationship. Therefore, when there are no common items in Ua and Ub voting records, then PCC(Ua, Ub) = 0 by default. In our approach, by using the absolute value of PCC, abs(PCC), we consider that both positively (those with similar ratings) and negatively correlated users (those with opposite tastes) might help2 to predict an active user’s final rating. The second criterion tries to penalize those highly correlated neighbors which are based on very few co-rated items, which have proved to be bad predictors (Herlocker et al. 1999). We might therefore take into account the number of items that both Ua and Ub rated simultaneously, i.e. their overlap degree. In particular, we consider that the quality of Ub as the parent of variable Ua is directly related with the probability of a user Ua rating an item which has been also rated by Ub. This criterion can be defined by the following expression: 2 For instance, if whenever Ub rates as like Ua rates with dislike, then knowing that Ub had rated an item with like provides information about Ua’s possible rating. 123