Geometric associative memories and their applications to pattern classification

Associative memories (AMs) were proposed as tools usually used in the restoration and classification of distorted patterns. Many interesting models have emerged in the last years with this aim. In this chapter a novel associative memory model (Geometric Associative Memory, GAM) based on Conformal Geometric Algebra (CGA) principles is described. At a low level, CGA provides a new coordinate-free framework for numeric processing in problem solving. The proposed model makes use of CGA and quadratic programming to store associations among patterns and their respective class. To classify an unknown pattern, an inner product is applied between it and the obtained GAM. Numerical and real examples to test the proposal are given. Formal conditions are also provided that assure the correct functioning of the proposal.