Genetic Algorithms for Feature Weighting in Multi-criteria Recommender Systems Chein-Shung hwang Each chromosome x is tested repeatedly, I times, by a leave-one-out cross validation. Pa. and ra. are the predicted and the actual overall ratings of user ua to item ij, respectively The overall prediction can be made by two different approaches, the filter-based and the wrapper based approach, depending on whether the method uses feedback from the subsequent MP module The filter-based method contains algorithms that use no input other than users'own ratings to calculate the overall predictions, whereas the wrapper-based approach uses feedback (i.e. the predicted ratings) from the MP module to facilitate the prediction For the filter-based approach, the predicted overall rating is calculated as a weighted sum o individual original ratings Wr where r. is the actual rating of user u, to item i, for criterion k For the wrapper-based approach, the predicted overall rating is calculated as a weighted sum of individual predicted ratings generated by the MP module n2×p w where Pa, is the predicted rating of user u, to item i for criterion k For each generation evolution, chromosomes for the next generation are selected using the roulette wheel selection scheme to implement proportionate random selection. All of the chromosomes are then paired up using the single-point crossover strategy with a probability Pe After the crossover, for each of the genes of the chromosomes, the gene is mutated with a probability Pm. The algorithm continues to evolve until a maximum number of generations is reached. The chromosome with the highest fitnes value is then selected as the optimal set of feature weights for active user u 4. 2. Multi-Criteria Prediction Module In the MP module, we decompose k-dimensional multi-criteria rating space into k single-rating recommendation problems and use a traditional user-based CF technique to estimate ratings for each criterion. Thus, we decompose the multi-criteria rating matrix R into k single-criterion rating matrices R. The CF algorithm is then implemented k times, one for each criterion. For each R",we first compute the similarity simar between active user u, and other users u, using the Pearson Correlation Method and then estimate the rating value pa for unrated item i using an adjusted 4.3. Recommendation model The goal of the RC module is to produce a recommendation list for an active user. RC modules first edict each unknown overall rating Pay directly by using the feature weight function estimated in the AG module and the multi-criteria rating value Pa estimated in the MP moduleGenetic Algorithms for Feature Weighting in Multi-criteria Recommender Systems Chein-Shung Hwang Each chromosome x is tested repeatedly, l times, by a leave-one-out cross validation. 0 ja p , and 0 jar , are the predicted and the actual overall ratings of user ua to item ij, respectively. The overall prediction can be made by two different approaches, the filter-based and the wrapper￾based approach, depending on whether the method uses feedback from the subsequent MP module. The filter-based method contains algorithms that use no input other than users’ own ratings to calculate the overall predictions, whereas the wrapper-based approach uses feedback (i.e. the predicted ratings) from the MP module to facilitate the prediction. For the filter-based approach, the predicted overall rating is calculated as a weighted sum of individual original ratings. ∑ ∑ = = × = 4 1 4 0 1 k k x k k ja k x ja w rw p , , (6) where k jar , is the actual rating of user a u to item ij for criterion k. For the wrapper-based approach, the predicted overall rating is calculated as a weighted sum of individual predicted ratings generated by the MP module. ∑ ∑ = = × = 4 1 4 0 1 k k x k k ja k x ja w pw p , , (7) where k ja p , is the predicted rating of user ua to item ij for criterion k. For each generation evolution, chromosomes for the next generation are selected using the roulette wheel selection scheme to implement proportionate random selection. All of the chromosomes are then paired up using the single-point crossover strategy with a probability pc. After the crossover, for each of the genes of the chromosomes, the gene is mutated with a probability pm. The algorithm continues to evolve until a maximum number of generations is reached. The chromosome with the highest fitness value is then selected as the optimal set of feature weights for active user ua . 4. 2. Multi-Criteria Prediction Module In the MP module, we decompose k-dimensional multi-criteria rating space into k single-rating recommendation problems and use a traditional user-based CF technique to estimate ratings for each criterion. Thus, we decompose the multi-criteria rating matrix R into k single-criterion rating matrices k R . The CF algorithm is then implemented k times, one for each criterion. For each k R , we first compute the similarity k ar sim between active user ua and other users ur using the Pearson Correlation Method and then estimate the rating value k aj p for unrated item j i using an adjusted weighted sum approach. 4. 3. Recommendation Model The goal of the RC module is to produce a recommendation list for an active user. RC modules first predict each unknown overall rating 0 aj p directly by using the feature weight function estimated in the AG module and the multi-criteria rating value k aj p estimated in the MP module. 130