Genetic Algorithms for Feature Weighting in Multi-criteria Recommender Systems Chein-Shung hwang 5. Loop] Go to step 2 3. Traditional collaborative filtering CF recommends items based on the historical ratings data of similar users. There are two major approaches for CF: user-based (also called memory-based)and model-based. User-based CF identifies users whose interests are similar to an active user and recommends items they like. Model-based CF infers a compact model and then uses it for recommendations. Here we describe the user-based CF In a typical CF scenario, there is a list of n users U=( uI, u2,..., u), a list of m items trix of ratings R=Ir], where r, represents the rating of user u, for item i, CF systems usually consist of two phases: neighborhood formation and prediction computation. In neighborhood formation, the similarity between the active user ua and other users u, is computed. There are two common methods to compute the similarity between users: Pearson correlation and cosine similarity. Pearson correlation measures the extent to which two variables linearly relate with each other. The Pearson correlation between users u and u. is defined as ∑(a-F)(-7) ∑(-元)2∑(-元) where /(a, r)represents the items that both user u, and u, have rated and ra and Fr represent the average rating of users u, and u,, respectively. The cosine similarity views the rating of each user as a multidimensional vector and computes the cosine value between the two vectors i∈(a,r) Once the similarities between active user u, and other users u, are computed, a subset of the nearest neighbors of u, are chosen based on the similarity measure, and the ratings of neighbors are ggregated to generate predictions for the active user. We consider two popular ways to average the ng. The first is the weighted sum approach Pa.j and the second is the adjusted weighted sum approach r∈N(a) I sima I where Pa. represents the prediction for the active user u, for item i, and M(a) represents the set ofGenetic Algorithms for Feature Weighting in Multi-criteria Recommender Systems Chein-Shung Hwang 5. [Loop] Go to step 2. 3. Traditional collaborative filtering CF recommends items based on the historical ratings data of similar users. There are two major approaches for CF: user-based (also called memory-based) and model-based. User-based CF identifies users whose interests are similar to an active user and recommends items they like. Model-based CF infers a compact model and then uses it for recommendations. Here we describe the user-based CF approach [12]. In a typical CF scenario, there is a list of n users U={ uuu n ,,, 21 }, a list of m items I={ m ,,, iii 21  }, and a matrix of ratings R=[ ij r ] , where ij r represents the rating of user ui for item j i . CF systems usually consist of two phases: neighborhood formation and prediction computation. In neighborhood formation, the similarity between the active user a u and other users r u is computed. There are two common methods to compute the similarity between users: Pearson correlation and cosine similarity. Pearson correlation measures the extent to which two variables linearly relate with each other. The Pearson correlation between users ua and ur is defined as ∑∑ ∑ ∈ ∈ ∈ − − −− = ),( , ),( , ),( , , , )()( ( )( ) raIi rir raIi aia raIi riraia ra rrrr rrrr sim 2 2 (1) where raI ),( represents the items that both user ua and ur have rated and ar and rr represent the average rating of users ua and ur , respectively. The cosine similarity views the rating of each user as a multidimensional vector and computes the cosine value between the two vectors. ∑∑ ∑ ∈ ∈ ∈ × = ),( , ),( , ),( ,, , raIi ir raIi ia raIi iria ra rr rr sim 2 2 (2) Once the similarities between active user ua and other users ur are computed, a subset of the nearest neighbors of ua are chosen based on the similarity measure, and the ratings of neighbors are aggregated to generate predictions for the active user. We consider two popular ways to average the rating. The first is the weighted sum approach: ∑ ∑ ∈ ∈ × = )( , )( ,, , || aNr ra aNr jrra ja sim rsim p (3) and the second is the adjusted weighted sum approach: ∑ ∑ ∈ ∈ −× += )( , )( ,, , || )( aNr ra aNr rjrra aja sim rrsim rp (4) where p , ja represents the prediction for the active user ua for item j i and N(a) represents the set of 128