Recommender Systems Clustering Using Bayesian Non Negative Matrix Factorization

Abstract

Recommender Systems present a high-level of sparsity in their ratings matrices. The collaborative filtering sparse data makes it difficult to: 1) compare elements using memory-based solutions; 2) obtain precise models using model-based solutions; 3) get accurate predictions; and 4) properly cluster elements. We propose the use of a Bayesian non-negative matrix factorization (BNMF) method to improve the current clustering results in the collaborative filtering area. We also provide an original pre-clustering algorithm adapted to the proposed probabilistic method. Results obtained using several open data sets show: 1) a conclusive clustering quality improvement when BNMF is used, compared with the classical matrix factorization or to the improved KMeans results; 2) a higher predictions accuracy using matrix factorizationbased methods than using improved KMeans; and 3) better BNMF execution times compared with those of the classic matrix factorization, and an additional improvement when using the proposed pre-clustering algorithm.

Keywords

• Bayesian NMF
• collaborative filtering
• hard clustering
• matrix factorization
• pre-clustering
• recommender systems