MATHEMATICAL AND ALGORITHMIC APPROACHES TO THE DEVELOPMENT OF A COLLABORATIVE FILTERING-BASED RECOMMENDER SYSTEM

Abstract

The article examines the mathematical and algorithmic support of a recommender system based on the collaborative filtering method. The relevance of the study is associated with the growth of digital content volumes and the need for automated generation of personalized recommendations for users. A movie recommender system is considered as the subject area; however, the proposed model can also be applied to other types of objects, such as products, books, musical compositions, educational resources, and information materials.

The main focus is on constructing a mathematical model of user preferences, forming a rating matrix, determining similarity between objects, and developing an algorithm for ranking recommendations. The study uses an item-based collaborative filtering approach, in which recommendations are generated based on the similarity between objects calculated from user ratings. Cosine similarity is used as the proximity measure, while the k-nearest neighbors algorithm is applied to find the most similar objects.

The proposed approach makes it possible to represent a recommender system not only as a software implementation but also as a mathematical and algorithmic model for processing incomplete and sparse data. The model includes a set of users, a set of objects, a preference matrix, a similarity function, a rule for selecting nearest objects, and a procedure for generating Top-N recommendations.