A new similarity measure for collaborative filtering based recommender systems

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The objective of a recommender system is to provide customers with personalized recommendations while selecting an item among a set of products (movies, books, etc.). The collaborative filtering is the most used technique for recommender systems. One of the main components of a recommender system based on the collaborative filtering technique, is the similarity measure used to determine the set of users having the same behavior with regard to the selected items. Several similarity functions have been proposed, with different performances in terms of accuracy and quality of recommendations. In this paper, we propose a new simple and efficient similarity measure. Its mathematical expression is determined through the following paper contributions: 1) transforming some intuitive and qualitative conditions, that should be satisfied by the similarity measure, into relevant mathematical equations namely: the integral equation, the linear system of differential equations and a non-linear system and 2) resolving the equations to achieve the kernel function of the similarity measure. The extensive experimental study driven on a benchmark datasets shows that the proposed similarity measure is very competitive, especially in terms of accuracy, with regards to some representative similarity measures of the literature.