  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, 864K items and 2
million 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.
