论文标题
核I：推荐系统和下降中的邻接光谱
Nucleus I: Adjunction spectra in recommender systems and descent
论文作者
论文摘要
推荐系统使用使用矩阵的概念分析来构建用户配置文件。这些概念被挖掘为光谱并形成Galois连接。下降是代数几何和拓扑中光谱分解的一般方法，这也导致了广义的Galois连接。推荐系统和下降理论都是庞大的研究领域，其技术差距如此之大，以至于试图建立链接似乎愚蠢。然而，正式的联系自下而上就出现了，反对作者的意图和更好的判断。熟悉的数据分析问题导致了类别理论的新解决方案。本文源于一系列早期的努力，以提供这些发展的自上而下的描述。
Recommender systems build user profiles using concept analysis of usage matrices. The concepts are mined as spectra and form Galois connections. Descent is a general method for spectral decomposition in algebraic geometry and topology which also leads to generalized Galois connections. Both recommender systems and descent theory are vast research areas, separated by a technical gap so large that trying to establish a link would seem foolish. Yet a formal link emerged, all on its own, bottom-up, against authors' intentions and better judgment. Familiar problems of data analysis led to a novel solution in category theory. The present paper arose from a series of earlier efforts to provide a top-down account of these developments.
