Recommender System research suffers currently from a disconnect between the size of academic data sets and the scale of industrial production systems. In order to bridge that gap we propose to generate more massive user/item interaction data sets by expanding pre-existing public data sets. User/item incidence matrices record interactions between users and items on a given platform as a large sparse matrix whose rows correspond to users and whose columns correspond to items. Our technique expands such matrices to larger numbers of rows (users), columns (items) and non zero values (interactions) while preserving key higher order statistical properties. We adapt the Kronecker Graph Theory to user/item incidence matrices and show that the corresponding fractal expansions preserve the fat-tailed distributions of user engagements, item popularity and singular value spectra of user/item interaction matrices. Preserving such properties is key to building large realistic synthetic data sets which in turn can be employed reliably to benchmark Recommender Systems and the systems employed to train them. We provide algorithms to produce such expansions and apply them to the MovieLens 20 million data set comprising 20 million ratings of 27K movies by 138K users. The resulting expanded data set has 10 billion ratings, 2 million items and 864K users in its smaller version and can be scaled up or down. A larger version features 655 billion ratings, 7 million items and 17 million users.
翻译:为了缩小这一差距,我们建议通过扩大原有的公共数据集来生成更大规模的用户/项目互动数据集。用户/项目频谱矩阵记录用户和特定平台上的项目之间的相互作用,将其作为一个庞大的稀少的矩阵,其行与用户相对应,其列与项目相对应。我们的技术将这种矩阵扩大到更多的行(用户)、列(项目)和非零值(互动),同时保留重要的更高顺序统计属性。我们将克伦克尔图理论调整为用户/项目事件矩阵,并表明相应的分形扩展保留用户参与、项目受欢迎程度和用户/项目互动矩阵的单一价值光谱的胖零售分布。保存这些属性是建立大型现实的合成数据集的关键,而这些数据集反过来可以可靠地用于为建议系统以及用于培训它们的系统进行基准。我们提供算法,以产生这种扩展并将其应用到由188K用户对27K电影评分2 000万分级组成的2 000万个数据集,由此而扩大的用户和升级的版本为845万分级和升级为100万分级。