in Movielens. We compare the following similarity measures: any traditional metric used. This fact must be emphasized since Pearson correlation(COR), cosine(COS), Mean Squared Differences the new latter similarity metrics which are usually proposed (MSD)and the similarity measure obtained with our GA-method improve the Mae while resulting in a worse coverage[ 7. while In this experiment, we have first divided the users in Movielens Graphic la shows that the best results in MAE with the GA- into two subsets: a subset of 1204 (20% of users which are re- method are obtained when using a small value in K, graphic garded as test users in Section 4. 1); and the subset of the rest of 1b shows that the best results with the ga-method are obtained users(80% users, 4832 users). Once divided the database, we have n coverage using medium values in K In this way, we shoul calculated the similarity measure between each user in the first use intermediate values in K(KE(150,., 200)) for obtaining subset of 20% users and each user in the second subset of 80% he most satisfactory results both in MAE and in coverage. Graphics 1c and 1d inform respectively about the precision and recall. These quality me e improved for any value used 5. Results in the number of recommendations, N. Consequently, the GA- method improves not only the accuracy and the coverage, but 5.1. Prediction and recommendation results also provides better recommendations. FilmAffinity: The results obtained with this database provide In this section we show the results obtained using the databases similar results to the one obtained for the database movielens specified in Table 1. Figs. 1-3 show respectively the results ob- As illustrated in Graphic 2a, we can see that our GA-method tained with Movielens, FilmAffinity and Netflix. As may be seen does not provide so good results in MAE with low K for this in these figures, the results obtained for all the quality measures database as for MovieLens. However, it provides better results (MAE, coverage, precision and recall) with our genetic algorithm when using high values in K. The reader must observe that are better that the ones obtained with the traditional metrics the ranking values used in FilmAffinity are larger((1,., 10)) Next, we will analyze the results according to the three than the ones used in movielens As may be seen in Graphic 2b, our GA-method provides best lev- els in coverage. In the same way, the results obtained for preci- Movielens: Graphic 1a informs about the mae error obtained sion and recall (see Graphics 2c and 2d)in this database are for Movielens when applying Pearson correlation(COR), cosine similar to the ones obtained for the movielens database (COS), Mean Squared Differences(MSD )and the 20 runs of the Netilix: The results obtained with this database may be used to GA-method. The GA-metric leads to fewer errors, particularly state that our method can be used for a rS with a large amount the most used values of K. the black dashed and continuous of data(see Table 1). Our method provides similar results for lines represent respectively the worst and the best result this database to the ones obtained for previous databases in obtained in the 20 times the GA method is run. The grey area both quality prediction measures(MAE and coverage)and qual ontains the area between these lines ity recommendation measures(precision and recall). Neverthe- Graphic 1b informs about the coverage obtained. As may b less, we must emphasize that regarding both MaE (graphic 3a) seen, our GA-method can improve the coverage for any value and precision(graphic 3c)our GA method shows improvements of k(the number of neighbors for each user) in relation when used in connection to this database a BestGA . WorstGA-COR--COS- MSD b 一 BestGA -.worstGA-COR·cos-MsD 呙导导昌器 8导导昌器員員昌 K-Neighbors BestGA --WorstGA-COR--COS-MSD d BestGA -.WorstGA-COR--COS-MSD 038 036 Traditional metrics and proposed genetic similarity method comparative results using Movielens: (a)accuracy(Mean Absolute Error). (b) coverage, (c)precision, (d)in Movielens. We compare the following similarity measures: Pearson correlation (COR), cosine (COS), Mean Squared Differences (MSD) and the similarity measure obtained with our GA-method. In this experiment, we have first divided the users in Movielens into two subsets: a subset of 1204 (20% of users which are re￾garded as test users in Section 4.1); and the subset of the rest of users (80% users, 4832 users). Once divided the database, we have calculated the similarity measure between each user in the first subset of 20% users and each user in the second subset of 80% users. 5. Results 5.1. Prediction and recommendation results In this section we show the results obtained using the databases specified in Table 1. Figs. 1–3 show respectively the results ob￾tained with Movielens, FilmAffinity and Netflix. As may be seen in these figures, the results obtained for all the quality measures (MAE, coverage, precision and recall) with our genetic algorithm are better that the ones obtained with the traditional metrics. Next, we will analyze the results according to the three databases: Movielens: Graphic 1a informs about the MAE error obtained for Movielens when applying Pearson correlation (COR), cosine (COS), Mean Squared Differences (MSD) and the 20 runs of the GA-method. The GA-metric leads to fewer errors, particularly in the most used values of K. The black dashed and continuous lines represent respectively the worst and the best result obtained in the 20 times the GA method is run. The grey area contains the area between these lines. Graphic 1b informs about the coverage obtained. As may be seen, our GA-method can improve the coverage for any value of K (the number of neighbors for each user) in relation to any traditional metric used. This fact must be emphasized since the new latter similarity metrics which are usually proposed improve the MAE while resulting in a worse coverage [7]. While Graphic 1a shows that the best results in MAE with the GA￾method are obtained when using a small value in K, Graphic 1b shows that the best results with the GA-method are obtained in coverage using medium values in K. In this way, we should use intermediate values in K (K 2 {150, ... , 200}) for obtaining the most satisfactory results both in MAE and in coverage. Graphics 1c and 1d inform respectively about the precision and recall. These quality measures are improved for any value used in the number of recommendations, N. Consequently, the GA￾method improves not only the accuracy and the coverage, but also provides better recommendations. FilmAffinity: The results obtained with this database provide similar results to the one obtained for the database Movielens. As illustrated in Graphic 2a, we can see that our GA-method does not provide so good results in MAE with low K for this database as for MovieLens. However, it provides better results when using high values in K. The reader must observe that the ranking values used in FilmAffinity are larger ({1, ... , 10}) than the ones used in Movielens. As may be seen in Graphic 2b, our GA-method provides best lev￾els in coverage. In the same way, the results obtained for preci￾sion and recall (see Graphics 2c and 2d) in this database are similar to the ones obtained for the MovieLens database. Netflix: The results obtained with this database may be used to state that our method can be used for a RS with a large amount of data (see Table 1). Our method provides similar results for this database to the ones obtained for previous databases in both quality prediction measures (MAE and coverage) and qual￾ity recommendation measures (precision and recall). Neverthe￾less, we must emphasize that regarding both MAE (graphic 3a) and precision (graphic 3c) our GA method shows improvements when used in connection to this database. Fig. 1. Traditional metrics and proposed genetic similarity method comparative results using Movielens: (a) accuracy (Mean Absolute Error), (b) coverage, (c) precision, (d) recall. 1314 J. Bobadilla et al. / Knowledge-Based Systems 24 (2011) 1310–1316