Efficient collaborative filtering recommendations with multi-channel feature vectors

Feature vectors and similarity measures are the two key issues of most existing collaborative filtering (CF) algorithms. In item-based CF algorithms, the feature vector is often defined as the ratings of all users for a given item. For a recommender system with n users, m items, and c ratings, the length of the feature vector is n; hence, the time complexity of the similarity computation is O(n). Consequently, the overall time complexity is \(O(m^2n^2)\), which may be computationally prohibitive for recommender systems with millions of users. In this paper, we define the multi-channel feature vector (MCFV), which is a vector of channel length c, and calculate the similarity between items using the respective MCFVs. Each element of an MCFV corresponds to the number of users with respective ratings for the item. The time complexity for the similarity computation is O(c), and the overall time complexity is \(O(m^2nc)\) when the k-nearest neighbors and weighted average algorithms are used. Experiments were conducted on four movie recommender systems, where n ranges from a few hundred to half a million, and c is five. Results show that the recommendation algorithms using our new similarity measure are significantly faster than their counterparts without sacrificing prediction accuracy in terms of mean absolute error and root mean square error.