Математичне обґрунтування алгоритму кластеризації користувачів у рекомендаційних системах

Abstract

У роботі розглянуто математичні основи алгоритмів кластеризації для рекомендаційних систем.

This paper examines the mathematical foundations of clustering algorithms for recommender systems. A comparative analysis of k-means, spectral clustering, and the Louvain algorithm is conducted in terms of their effectiveness for grouping users with similar preferences. The objective functions optimized by each algorithm are investigated, and their application for different types of user data is substantiated. A modification of spectral clustering is proposed that improves the accuracy of recommendations for social networks by optimizing the normalized cut of the graph. Experimental results demonstrate a 12% improvement in recommendation quality when applying the modified algorithm compared to the classical approach.