Projection Pursuit via Multivariate Histograms

: The problem of finding the most interesting low dimensional subspaces of a multidimensional data set has usually been formulated as a search for the maximum over all projection subspaces of a measure of information. Alternatively, interesting subspaces may be characterized as the eigenspaces associated to the largest eigenvalues of a tensor valued information measure on the whole space. Since this same information measure solves the problem of the asymptotically optimal multivariate histogram, the issues of selection and representation are resolved simultaneously. This leads to substantial simplification of both the computational and conceptual problems in projection pursuit.