Popularity The model is created considering all the users in the training UPL First80 NoFirst80 set. The users in the test set are divided according to the 3 groups previously defined. In Table 1(a)we select all users 2922.2% 6.9% ith at least 2 ratings to create the model by means of naive 10-1924.1%0.1% bayesian networks. In Table 1(b) and 1(c)we create the 10.1% model using users with a more rich profile, i.e., with at least 10 and 20 ratings, respectively. The test considers again all Table 1. Recall obtained with the SVd algo the users. This allows to see if a more rich and compact rithm with L=15 on the nm dataset. Model model can improve recommendations ings. UPL stands for User Profile Length. Qt created with users who have at least 2 6. Conclusions RS are a powerful technology: they help both users to find what they want and e-commerce companies to improve related to a specific value of the latent size L of SVD al- their sales gorithm. In the same graph it is also represented a tri Each recommender algorithm may behave in different recommendation algorithm, used as a term of comparison, ways with respect to different datasets. Given a dataset, by means of the methodology proposed in this paper we can putes, for each item, the mean of all its ratings. Then, it analyze the behavior of different recommender algorithms creates a sorted list of items according to such mean values On the basis of several results obtained. we can declare This list is used for the recommendation to all users. Each that a rs should have different models to make recommen- point of the ROC curve represents a pair(FPR, TPR)related dations to different groups of users and with respect to the to a specific threshold. In this case the value of the thresh- popularity of the items Id is in the range(1.5). For example, in Figure 5 we highlight the points related to the threshold equal to 3. The best curve is obtained by setting the latent size L to 1 References ROC2 technique. According to Section 3.2, we ap- ply rOC2 techique in order to optimize S VD algorithm or [1] Readings in Information Retrieval. Morgan Kaufman the binary dataset NM. Figure 6(a) shows an application of the rOC2 techinque, where the model is generated usin [2 C. Basu, H. Hirsh, and w. Cohen. Recommendation as all users but predictions are made only for users who have classification: Using social and content-based information in recommendation. Proceedings of the Fifteenth National rated between 2 and 9 items. It is also shown the curve corresponding to the top-rated recommendation, that is we Conference on Artificial Intelligence, 714720, 1998 [3 J. Bennett and S Lanning. The Netflix Prize. Proceedings recommend to each user the most rated items, in popular- of KDD Cup and Workshop, 2007 ity order. The model with a latent size of 15 is the best [4] M. Berry, S. Dumais, and G. O'Brien. Using Linear Al- one. For each curve we highlight 2 points that correspond gebra for Intelligent Information Retrieval. SIAM Revie to N=5 and N= 20, respectively. If the dataset is not bi 7(4):573-595,1995 nary we can use, for example, the result obtained by means [5] D. Billsus and M. Pazzani. Learning collaborative informa- of the ROCI technique. Figure 6(b) shows that 15 is again tion filters. Proceedings of the Fifteenth International Con the best value for parameter L. Figure 6(c) shows again the ference on Machine Learning, 54, 1998 pplication of the ROC2 technique, but on the NM dataset [6] C. Bishop. Pattern recognition and machine learning when the NBN algorithm is adopted. The model is created Springer, 2006 [7] J Breese. D. Heckerman, C. Kadie, et al. Empirical analysis using all the user with a number of rating greater or equal of predictive algorithms for collaborative filtering. Proceed- than 2. B of this model we compute the prediction ings of the Fourteenth Conference on Uncertainty in Artifi- for the three groups of users. In any case, the best predic tion is obtained for users having ratings into the range of [8] A. Buczak, J. Zimmerman, and K. Kurapati. Personaliza- 2..9 tion: Improving Ease-of-Use, Trust and Accuracy of a TV Show Recommender. Proceedings of the AH'2002 Work 5.3. Computation of recall TV,2002. 9] D. Chickering, D. Geiger, and D. Heckerman. Learning Bayesian networks is NP-hard. e use the recall in order to compare the quality of the [101 M. Deshpande and G Karypis. Item-based top-N recom- algorithms described in Section 4. Table 1 shows the recall mendation algorithms. ACM Transactions on information obtained applying the SVD algorithm on the NM dataset. Systems(TO/S),22(1):143-177,2004Popularity UPL First80 NoFirst80 2-9 22.2% 6.9% 10-19 24.1% 0.1% ≥ 20 25.7% 10.1% Table 1. Recall obtained with the SVD algo￾rithm with L=15 on the NM dataset. Model created with users who have at least 2 rat￾ings. UPL stands for User Profile Length. related to a specific value of the latent size L of SVD al￾gorithm. In the same graph it is also represented a trivial recommendation algorithm, used as a term of comparison, called Average Recommender (AR). This algorithm com￾putes, for each item, the mean of all its ratings. Then, it creates a sorted list of items according to such mean values. This list is used for the recommendation to all users. Each point of the ROC curve represents a pair (FPR,TPR) related to a specific threshold. In this case the value of the thresh￾old is in the range (1 . . . 5). For example, in Figure 5 we highlight the points related to the threshold equal to 3. The best curve is obtained by setting the latent size L to 15. ROC2 technique. According to Section 3.2, we ap￾ply ROC2 techique in order to optimize SVD algorithm on the binary dataset NM. Figure 6(a) shows an application of the ROC2 techinque, where the model is generated using all users but predictions are made only for users who have rated between 2 and 9 items. It is also shown the curve corresponding to the top-rated recommendation, that is we recommend to each user the most rated items, in popular￾ity order. The model with a latent size of 15 is the best one. For each curve we highlight 2 points that correspond to N = 5 and N = 20, respectively. If the dataset is not bi￾nary we can use, for example, the result obtained by means of the ROC1 technique. Figure 6(b) shows that 15 is again the best value for parameter L. Figure 6(c) shows again the application of the ROC2 technique, but on the NM dataset when the NBN algorithm is adopted. The model is created using all the user with a number of rating greater or equal than 2. By means of this model we compute the prediction for the three groups of users. In any case, the best predic￾tion is obtained for users having ratings into the range of [2 . . . 9]. 5.3. Computation of recall We use the recall in order to compare the quality of the algorithms described in Section 4. Table 1 shows the recall obtained applying the SVD algorithm on the NM dataset. The model is created considering all the users in the training set. The users in the test set are divided according to the 3 groups previously defined. In Table 1(a) we select all users with at least 2 ratings to create the model by means of naive bayesian networks. In Table 1(b) and 1(c) we create the model using users with a more rich profile, i.e., with at least 10 and 20 ratings, respectively. The test considers again all the users. This allows to see if a more rich and compact model can improve recommendations. 6. Conclusions RS are a powerful technology: they help both users to find what they want and e-commerce companies to improve their sales. Each recommender algorithm may behave in different ways with respect to different datasets. Given a dataset, by means of the methodology proposed in this paper we can analyze the behavior of different recommender algorithms. On the basis of several results obtained, we can declare that a RS should have different models to make recommen￾dations to different groups of users and with respect to the popularity of the items. References [1] Readings in Information Retrieval. Morgan Kaufmann, 1997. [2] C. Basu, H. Hirsh, and W. Cohen. Recommendation as classification: Using social and content-based information in recommendation. Proceedings of the Fifteenth National Conference on Artificial Intelligence, 714720, 1998. [3] J. Bennett and S. Lanning. The Netflix Prize. Proceedings of KDD Cup and Workshop, 2007. [4] M. Berry, S. Dumais, and G. O’Brien. Using Linear Al￾gebra for Intelligent Information Retrieval. SIAM Review, 37(4):573–595, 1995. [5] D. Billsus and M. Pazzani. Learning collaborative informa￾tion filters. Proceedings of the Fifteenth International Con￾ference on Machine Learning, 54, 1998. [6] C. Bishop. Pattern recognition and machine learning. Springer, 2006. [7] J. Breese, D. Heckerman, C. Kadie, et al. Empirical analysis of predictive algorithms for collaborative filtering. Proceed￾ings of the Fourteenth Conference on Uncertainty in Artifi- cial Intelligence, 461, 1998. [8] A. Buczak, J. Zimmerman, and K. Kurapati. Personaliza￾tion: Improving Ease-of-Use, Trust and Accuracy of a TV Show Recommender. Proceedings of the AH’2002 Work￾shop on Personalization in Future TV, 2002. [9] D. Chickering, D. Geiger, and D. Heckerman. Learning Bayesian networks is NP-hard. [10] M. Deshpande and G. Karypis. Item-based top-N recom￾mendation algorithms. ACM Transactions on Information Systems (TOIS), 22(1):143–177, 2004