FP Lousame and e. sanchez Vector similarity is another weighting function that can be used to measure the similarity between users ∈R∩R1 Tki. rli Though Pearson correlation and vector similarity are the most popular, other metrics are also used. For instance, Shardanand and Maes 56 used a Mean Squared Difference to compute the degree of dissimilarity between users k and I and predictions were made by considering all users with a dissimilarity to the user which was less than a certain threshold and computing the weighted average of the ratings provided by the most similar users, where weights were inverse proportional to this dissimilarity. They also presented a Constrained Pearson correlation to take into account the positivity and negativity of ratings Most frequent item recommendation. Instead of using equation 2 to compute predictions and then construct a top-N ndation by selecting the highest predicted items, each similar item could be ranked according to how many similar Sk, j Uk/al.s= ind the recommendation list would be then computed by sorting the most fre- quently selected N items Weighting Schemes Breese et al. [15 investigated different modifications to the weighting function that have shown to improve performance of this memory-based approach Default voting was proposed as an extension of the Pearson correlation(equation 3)that improves the similarity measure in cases in which either the active user or the matching user have relatively few ratings(Rk n R has very few items) Refer to [15 for a mathematical formulation Inverse user frequency tries to reduce weights for commonly selected items based on the background idea that commonly selected items are not as useful in char acterizing the user as those items that are selected less frequently. Following the original concepts in the domain of information retrieval [10 the user inverse frequency can be defined as I ukI {uk:i∈Bk where ni is the number of users who rated item i and n is the total number f users in the database. To use the inverse user frequency in equation 4 the transformed rating is simply the original rating multiplied by the user inverse frequency. It can also be used in correlation but the transformation is not direct (see Breese et al. [15 for a detailed description)86 F.P. Lousame and E. S´anchez Vector similarity is another weighting function that can be used to measure the similarity between users: wk,l = i∈Rk∩Rl rki · rli i∈Rk∩Rl r2 ki i∈Rk∩Rl r2 li (4) Though Pearson correlation and vector similarity are the most popular, other metrics are also used. For instance, Shardanand and Maes [56] used a Mean Squared Difference to compute the degree of dissimilarity between users k and l and predictions were made by considering all users with a dissimilarity to the user which was less than a certain threshold and computing the weighted average of the ratings provided by the most similar users, where weights were inverse proportional to this dissimilarity. They also presented a Constrained Pearson correlation to take into account the positivity and negativity of ratings in absolute scales. Most frequent item recommendation. Instead of using equation 2 to compute predictions and then construct a top-N recommendation by selecting the highest predicted items, each similar item could be ranked according to how many similar users selected it sk,j =  l∈Uk/al,j=1 1 (5) and the recommendation list would be then computed by sorting the most fre￾quently selected N items. Weighting Schemes Breese et al. [15] investigated different modifications to the weighting function that have shown to improve performance of this memory-based approach: Default voting was proposed as an extension of the Pearson correlation (equation 3) that improves the similarity measure in cases in which either the active user or the matching user have relatively few ratings (Rk ∩ Rl has very few items). Refer to [15] for a mathematical formulation. Inverse user frequency tries to reduce weights for commonly selected items based on the background idea that commonly selected items are not as useful in char￾acterizing the user as those items that are selected less frequently. Following the original concepts in the domain of information retrieval [10] the user inverse frequency can be defined as: fi = log | {uk} | | {uk : i ∈ Bk} | = log n ni (6) where ni is the number of users who rated item i and n is the total number of users in the database. To use the inverse user frequency in equation 4 the transformed rating is simply the original rating multiplied by the user inverse frequency. It can also be used in correlation but the transformation is not direct (see Breese et al. [15] for a detailed description).