Analysis and Visualization of the Parameter Space of Matrix Factorization-based Recommender Systems

Recommender system is the most successful commercial technology in the past decade. Technical mammoth such as Temu, TikTok and Amazon utilize the technology to generate enormous revenues each year. Although there have been enough research literature on accuracy enhancement of the technology, explainable AI is still a new idea to the field. In 2022, the author of this paper provides a geometric interpretation of the matrix factorization-based methods and uses geometric approximation to solve the recommendation problem. We continue the research in this direction in this paper, and visualize the inner structure of the parameter space of matrix factorization technologies. We show that the parameters of matrix factorization methods are distributed within a hyper-ball. After further analysis, we prove that the distribution of the parameters is not multivariate normal.