J Bobadilla et al. / Knowledge-Based Systems 23(2010)520-528 A 210000000 5000000 Fig. 1. Distribution of votes in RS: (A)MovieLens 1M and(B)NetFlix. B 8:eesN8罚罚导守导导日 8ssN:s。9导守导导日 Arithmetic average 0m0mmmmg 500 8ss=s:ssN:89罚导守守导导日 Nq。da。Nqda。。ta。Nqa。 Standard deviation Fig. 2. Arithmet rage and standard deviation on the MovieLens IM and Net Flix ratings of the items (A)MovieLens arithmetic average, ( B)Net Flix arithmetic average, (c) lovieLens standard deviation,(D) NetFlix standard deviation. to represent a positive or non-positive rating of the items, and to a the precision when the number of recommendations(N)is high. lesser extent a range of these ratings; for instance, in a rS with pos- The numerical key to this improvement lies in the improved sible votes situated in the interval [1.5], a 4 will generally repre- capacity of the discrete calculation to determine whether an item sent a positive rating, which in some cases will be reinforced is recommended(based on the number of k-neighborhoods with with the rating 5. Similarly, a 3 will represent a non-positive rating, value P in that item), as regards the calculation with numerical In order to test this hypothesis, we have designed an experi- approach on the numerical values of the vote lected aggregation which in some cases will be reinforced with the rating 2 or 1 votes into P votes(Positive)and all of 1, 2 and 3 votes into N votes (Non-positive), in such a way that we aim to measure the impact Pearson -Positive/ Non- made on the recommendations by doing without the detailed information provided by the numerical values of the votes In the experiment we compare the precision/recall obtained in a egular way(using the numerical values of the votes )with that ob- tained using only the discretized values P and N: for this purpose we establish the relevance threshold at value 4 (0=4), assimilating a0.55 relevant"with"positive"; we use Pearson correlation, deviation om mean aggregation approach, 20% of test users, 20% of test items. number of recommendations from 2 to 20 K= 150. The experiment has been repeated for values between K= 100 and Rean05060708 K=200, obtaining equivalent results Fig 3 displays the results, which show how the"positive/non positive" discretization not only does not worsen the precision/re- results obtained using the numerical values. 20% of test users. 20% of test items. call measurements, but rather it improves them both, particularly K=150, Pearson correlation,0=4to represent a positive or non-positive rating of the items, and to a lesser extent a range of these ratings; for instance, in a RS with pos￾sible votes situated in the interval [1..5], a 4 will generally repre￾sent a positive rating, which in some cases will be reinforced with the rating 5. Similarly, a 3 will represent a non-positive rating, which in some cases will be reinforced with the rating 2 or 1. In order to test this hypothesis, we have designed an experi￾ment on the MovieLens 1M database: we transformed all 4 and 5 votes into P votes (Positive) and all of 1, 2 and 3 votes into N votes (Non-positive), in such a way that we aim to measure the impact made on the recommendations by doing without the detailed information provided by the numerical values of the votes. In the experiment we compare the precision/recall obtained in a regular way (using the numerical values of the votes) with that ob￾tained using only the discretized values P and N; for this purpose, we establish the relevance threshold at value 4 (h = 4), assimilating ‘‘relevant” with ‘‘positive”; we use Pearson correlation, deviation from mean aggregation approach, 20% of test users, 20% of test items, number of recommendations from 2 to 20, K = 150. The experiment has been repeated for values between K = 100 and K = 200, obtaining equivalent results. Fig. 3 displays the results, which show how the ‘‘positive/non￾positive” discretization not only does not worsen the precision/re￾call measurements, but rather it improves them both, particularly the precision when the number of recommendations (N) is high. The numerical key to this improvement lies in the improved capacity of the discrete calculation to determine whether an item is recommended (based on the number of k-neighborhoods with value P in that item), as regards the calculation with numerical values (prediction obtained by applying the selected aggregation approach on the numerical values of the votes and their subse￾quent thresholding). Fig. 1. Distribution of votes in RS: (A) MovieLens 1M and (B) NetFlix. Fig. 2. Arithmetic average and standard deviation on the MovieLens 1M and NetFlix ratings of the items. (A) MovieLens arithmetic average, (B) NetFlix arithmetic average, (C) MovieLens standard deviation, (D) NetFlix standard deviation. Fig. 3. Precision/recall obtained by transforming all 4 and 5 votes into P votes (positive) and all 1, 2 and 3 votes into N votes (non-positive), compared to the results obtained using the numerical values. 20% of test users, 20% of test items, K = 150, Pearson correlation, h = 4. 522 J. Bobadilla et al. / Knowledge-Based Systems 23 (2010) 520–528