The hyperbox

A hyperbox is a 2-dimensional depiction of an N-dimensional box (rectangular parallelepiped). This paper defines the visual syntax of hyperboxes, states some properties, and sketches two applications. Hyperboxes can be evocative visual names for tensors or multidimensional arrays in visual programming languages. They can also be used to simultaneously display all pairwise relationships in an N-dimensional dataset. We show that this can be helpful in choosing a sequence of dimension-reducing transformations that preserve interesting properties of the dataset.