A Recommender System (RS) consists of two basic entities: users and items, where users provide their opinions (ratings) about items. We denote these users by U = {u_1, u_2,..., u_M}, where the number of users using the system is |U| = M, and denote the set of items being recommended by I = {i_1,i_2,..., i_N}, with |I| = N. We can represent each element of user space U and item space I with a profile. We usually represent a user's profile by de fining their characteristics like age, gender, geographical location, etc.; however, in simple cases we represent it by a unique user Identifi er (ID). Similarly, we represent each item by de fining some characteristic; for example in a book recommender system, each book can be represented by author, topic, year of release, etc. Recommender systems store the history of the user's interactions with the system; for example, user purchase history, types of items they purchase together, their r...
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