COMPARATIVE ANALYSIS OF MATHEMATICAL MODELS OF COLLABORATIVE FILTERING IN THE DEVELOPMENT OF A MOVIE RECOMMENDER SYSTEM

Abstract

The article examines mathematical models used in the development of movie recommender systems, with a primary focus on collaborative filtering methods. The problem of predicting user preferences based on a sparse rating matrix is formalized. User-based and item-based models are compared, along with Euclidean similarity, Pearson correlation, cosine similarity, and the Jaccard coefficient, as well as the k-nearest neighbors model and matrix factorization methods. The practical part is based on a software implementation of item-based collaborative filtering using the cosine metric and CSR data representation. The experimental dataset includes 100,836 ratings provided by 610 users for 9,724 rated movies. To improve model robustness, threshold filtering was applied: only movies with at least 20 ratings and users with at least 40 ratings were included in the training dataset. Testing on three user profiles showed a 100% genre match between the generated recommendation lists and the dominant genre, no overlap between the recommendations of two users with the same dominant genre, and an average cosine distance ranging from 0.096 to 0.116. The obtained results confirm the model’s ability to account for individual rating patterns; however, they also reveal its dependence on the selection of the reference movie and the need for further comparison with SVD, ALS, and hybrid models.