Pattern Classification Based on Conformal Geometric Algebra and Optimization Techniques

Conformal Geometric Algebra (CGA) is a high level language commonly used in mathematical, physics and engineering problems. At a top level, CGA is a free coordinate tool for designing and modeling geometric problems; at a low level CGA provides a new coordinate framework for numeric processing in problem solving. In this paper we show how to use quadratic programming and CGA for, given two sets p and g of points in R(n), construct an optimal separation sphere S such that, all points of p are contained inside of it, and all points of g are outside. To classify an unknown pattern x, an inner product must be applied between x and S. Some numerical and real examples to test the proposal are given.