Steering high order moment calculations from lower dimensional spaces

Abstract

In this study we consider some well established algorithms used to determine separating hyperplanes for sets in R n . We implement these algorithms in a high dimensional tensor space that is affiliated with representing the higher order moment information for the sets in question. We identify an inner product preserving morphism from tensor space to R n . Using the morphism, the calculations of the algorithm are brought down to a space of much lower dimension. Our results make it clear that higher order moment computations can often avoid the burden of computation in a high dimensional vector space.