  Correspondence analysis (CA) is a multivariate statistical tool used to
visualize and interpret data dependencies. CA has found applications in fields
ranging from epidemiology to social sciences. However, current methods used to
perform CA do not scale to large, high-dimensional datasets. By re-interpreting
the objective in CA using an information-theoretic tool called the principal
inertia components, we demonstrate that performing CA is equivalent to solving
a functional optimization problem over the space of finite variance functions
of two random variable. We show that this optimization problem, in turn, can be
efficiently approximated by neural networks. The resulting formulation, called
the correspondence analysis neural network (CA-NN), enables CA to be performed
at an unprecedented scale. We validate the CA-NN on synthetic data, and
demonstrate how it can be used to perform CA on a variety of datasets,
including food recipes, wine compositions, and images. Our results outperform
traditional methods used in CA, indicating that CA-NN can serve as a new,
scalable tool for interpretability and visualization of complex dependencies
between random variables.
