M.Y.H. Al-Shamri, K.K. Bharadwaj/ Expert Systems with Applications 35(2008)1386-1399 and to supervise the learning process of FGRS, whereas 5.1. Experiment I the test ratings are treated as unseen ratings that the sys- tem would attempt to predict In this experiment we run the proposed FRS and com- Two evaluation metrics are used to evaluate the effec- pare its results with classical PRS. For PRS experiment, tiveness of different RS, the mean absolute error (MAE), if the correlation coefficient is negative, then users ux and and the total coverage of the system. The MAE measures ly are negatively correlated. This means that each user dis- the deviation of predictions generated by the rs from the courages the other. In our experiments, we follow the most true ratings specified by the user. The MAE() for active used strategy of keeping only positive correlation values user u; ( Breese et al., 1998; Vozalis Margaritis, 2003 )is because users with a negative correlation are dissimilar to given by the following formula the active user and hence it is better not to consider their ratings(Massa Avesani, 2004). The neighborhood set size is kept 30 for all the experiments MAE(O) lpr. (23) Usually, authors run PRS for a selected set of users only but in this experiment we run PRs over entire training users' database, even if it is time consuming. The difference where ni is the cardinality of the test ratings set of The total mae over all the active users, Nr(in our between gender(occupation) values is either 0, if the two users have the same gender(occupation) or I otherwise iments Nr= 50) can be calculated as This agrees with our reasoning for making opposite values MAE I as far as possible. Moreover, some sort of normalizatic MaE(O (24)(Han& Kamber, 2001)is used for age values to ensure that the values fall within the same range of GIM range, i.e. Lower MAE corresponds to more accurate predictions of a [0, 5]. Each age value is multiplied by(5/80), where age given RS. On the other hand, coverage is the measure of 80 is assumed to be the maximum possible age the percentage of items for which a RS can provide predic- The system picks the movies, from the test ratings set of tions. The RS may not be able to make predictions for the active user, one by one. Thereafter predicts ratings for every item. Low coverage value indicates that the RS will them using formula(4) over the set of all neighbors who not be able to assist the user with many of the items he have rated the same movie. After getting the predicted rat has not rated( Breese et al., 1998: Massa Avesani, ings, the system compares them with the actual ratings 2004). We compute coverage as the percentage of items given by the active user. Figs. 4 and 5 show the correct pre- over all users for which a prediction was requested and diction percentage obtained from PRS and FRS for the the system was able to produce a prediction(Vozalis& fifty active users of split-I(best split)and split-3(worst Margaritis, 2003) split), respectively. Each graph shows the percentage of the number of ratings that the system predicted correctly Coverage =siIP out of the total number of available test ratings by the lere, Pi is the total number of predicted items for active user Il; 5.1.1. Analysis of the results In the following two experiments, all the five splits of The implementation of PRS for 50 active users took data are used to show the effectiveness of the proposed user around 13 16 min, while it was around 2. 13 min only for model, fuzzy and hybrid fuzzy-genetic approaches to Rs. FRS for the same set of active users. The computational All experiments are conducted on a PC with 2.66 GHz Intel time complexity is reduced by approximately a factor of Pentium 4) CPU, 256MB RAM six with the proposed user model. Results summarized 830 20 s9s88NR588于导兽导 Active User ■FRs 口FGRs Fig 4. Correct prediction centage for active users of split-1and to supervise the learning process of FGRS, whereas the test ratings are treated as unseen ratings that the sys￾tem would attempt to predict. Two evaluation metrics are used to evaluate the effec￾tiveness of different RS, the mean absolute error (MAE), and the total coverage of the system. The MAE measures the deviation of predictions generated by the RS from the true ratings specified by the user. The MAE(i) for active user ui (Breese et al., 1998; Vozalis & Margaritis, 2003) is given by the following formula: MAEðiÞ ¼ 1 ni Xni j¼1 jpri;j ri;jj; ð23Þ where ni is the cardinality of the test ratings set of user ui. The total MAE over all the active users, NT (in our exper￾iments NT = 50) can be calculated as MAE ¼ 1 NT XNT i¼1 MAEðiÞ: ð24Þ Lower MAE corresponds to more accurate predictions of a given RS. On the other hand, coverage is the measure of the percentage of items for which a RS can provide predic￾tions. The RS may not be able to make predictions for every item. Low coverage value indicates that the RS will not be able to assist the user with many of the items he has not rated (Breese et al., 1998; Massa & Avesani, 2004). We compute coverage as the percentage of items over all users for which a prediction was requested and the system was able to produce a prediction (Vozalis & Margaritis, 2003) Coverage ¼ PNT i¼1 P pi NT i¼1ni : ð25Þ Here, pi is the total number of predicted items for active user ui. In the following two experiments, all the five splits of data are used to show the effectiveness of the proposed user model, fuzzy and hybrid fuzzy-genetic approaches to RS. All experiments are conducted on a PC with 2.66 GHz Intel (Pentium 4) CPU, 256MB RAM. 5.1. Experiment 1 In this experiment we run the proposed FRS and com￾pare its results with classical PRS. For PRS experiment, if the correlation coefficient is negative, then users ux and uy are negatively correlated. This means that each user dis￾courages the other. In our experiments, we follow the most used strategy of keeping only positive correlation values because users with a negative correlation are dissimilar to the active user and hence it is better not to consider their ratings (Massa & Avesani, 2004). The neighborhood set size is kept 30 for all the experiments. Usually, authors run PRS for a selected set of users only but in this experiment we run PRS over entire training users’ database, even if it is time consuming. The difference between gender (occupation) values is either 0, if the two users have the same gender (occupation) or 1 otherwise. This agrees with our reasoning for making opposite values as far as possible. Moreover, some sort of normalization (Han & Kamber, 2001) is used for age values to ensure that the values fall within the same range of GIM range, i.e. [0, 5]. Each age value is multiplied by (5/80), where age 80 is assumed to be the maximum possible age. The system picks the movies, from the test ratings set of the active user, one by one. Thereafter predicts ratings for them using formula (4) over the set of all neighbors who have rated the same movie. After getting the predicted rat￾ings, the system compares them with the actual ratings given by the active user. Figs. 4 and 5 show the correct pre￾diction percentage obtained from PRS and FRS for the fifty active users of split-1 (best split) and split-3 (worst split), respectively. Each graph shows the percentage of the number of ratings that the system predicted correctly out of the total number of available test ratings by the active user. 5.1.1. Analysis of the results The implementation of PRS for 50 active users took around 13.16 min, while it was around 2.13 min only for FRS for the same set of active users. The computational time complexity is reduced by approximately a factor of six with the proposed user model. Results summarized in 0 10 20 30 40 50 60 70 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Active User % of correct predictions PRS FRS FGRS Fig. 4. Correct predictions percentage for active users of split-1. M.Y.H. Al-Shamri, K.K. Bharadwaj / Expert Systems with Applications 35 (2008) 1386–1399 1395