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.

翻译：推荐系统是过去十年中最成功的商业技术。Temu、TikTok和亚马逊等技术巨头每年利用该技术创造巨额营收。尽管已有大量关于该技术精度提升的研究文献，可解释人工智能对该领域而言仍是一个新兴概念。2022年，本文作者提出了基于矩阵分解方法的几何解释，并利用几何近似方法解决推荐问题。本文延续这一研究方向，对矩阵分解技术参数空间的内部结构进行可视化分析。我们证明矩阵分解方法的参数分布于超球体内部。经进一步分析，我们证实参数分布并非多元正态分布。