  Low-rank approximations of data matrices are an important dimensionality
reduction tool in machine learning and regression analysis. We consider the
case of categorical variables, where it can be formulated as the problem of
finding low-rank approximations to Boolean matrices. In this paper we give what
is to the best of our knowledge the first integer programming formulation that
relies on only polynomially many variables and constraints, we discuss how to
solve it computationally and report numerical tests on synthetic and real-world
data.
