A Taxonomy of Collaborative-Based Recommender Syster Table 1. Summary of memory-based algorithms based on the different components of the recommendation process Neighborhood selection Prediction computation Pearson correlation User-based Ratings Rating aggregation (default voting) Most frequent item Mean squared difference Predictability Predictability co Linear rating transforma- Item-based Conditional probability. Rating aggregation (adjusted ratings)based similarity Item-to-item coo Cluster-based (cluster-based Pearson correlation Rating aggregation nothing trust of users Trust inferences Ratings Weighted average composi-.Rating aggregation Improved Ratings Weight optimization Rating aggregation This CF approach estimates unknown ratings based on recorded ratings of like- nded users. The predicted rating of the active user for item j is a weighted sum of ratings of other user (r1-) where Uk denotes the set of users in the database that satisfy wk, 1+0. This weights can reflect distance, correlation or similarity between each user and the active user. Fk and Fi represent the mean rating of the active user k and user L, espectively. Different weighting functions can be considered. Pearson correlation, cosine vector similarity, Spearman correlation, entropy-based uncertainty, mean-square difference are some examples. The Pearson correlation(eq. 3) was the first measure used to compute these weights 50. Breese et al. [15 and Herlocker et al.[27 proved that Pearson correlation performs better than other metrics (rk.i-7k)(r;-) I Note that Pearson correlation is defined in [1,+1] and then, in order to make sense sing negative weights, ratings should be re-scaled to fit [-r, +rlA Taxonomy of Collaborative-Based Recommender Systems 85 Table 1. Summary of memory-based algorithms based on the different components of the recommendation process Data (preprocessing) Neighborhood selection Prediction computation User-based Ratings (default voting) · Pearson correlation · Vector similarity → Inverse user frequency · Mean squared difference · Rating aggregation · Most frequent item Predictability paths Ratings · Predictability condition heuristics · Linear rating transforma￾tion Item-based Ratings (adjusted ratings) · Vector similarity · Pearson correlation · Conditional probability based similarity · Rating aggregation · Regression based Item-to-item coocurrence Cluster-based smoothing Ratings (cluster-based smoothing) · Pearson correlation · Rating aggregation Trust inferences Ratings · Compute trust of users → Pearson correlation Weighted average composi￾tion · Rating aggregation Improved neighborhood Ratings (remove global effects) · Weight optimization · Rating aggregation User-Based This CF approach estimates unknown ratings based on recorded ratings of like￾minded users. The predicted rating of the active user for item j is a weighted sum of ratings of other users, νk,j = ¯rk + l∈Uk wk,l · (rl,j − r¯l) l∈Uk |wk,l| (2) where Uk denotes the set of users in the database that satisfy wk,l = 0. This weights can reflect distance, correlation or similarity between each user and the active user. ¯rk and ¯rl represent the mean rating of the active user k and user l, respectively. Different weighting functions can be considered. Pearson correlation, cosine vector similarity, Spearman correlation, entropy-based uncertainty, mean-square difference are some examples. The Pearson correlation (eq. 3)1 was the first measure used to compute these weights [50]. Breese et al. [15] and Herlocker et al. [27] proved that Pearson correlation performs better than other metrics. wk,l = i∈Rk∩Rl (rk,i − r¯k)(rl,i − r¯l) i∈Rk∩Rl (rk,i − r¯k)2 i∈Rk∩Rl (rl,i − r¯l)2 (3) 1 Note that Pearson correlation is defined in [−1, +1] and then, in order to make sense when using negative weights, ratings should be re-scaled to fit [−r,+r].