Geometric Neural Computing

According to the literature, there are two mathematical systems used in neural computing: tensor algebra and matrix algebra. In contrast, the authors have chosen to use the coordinate-free system of Clifford or geometric algebra for the analysis and design of feed-forward neural networks. Our work shows that real-, complex-, and quaternion-valued neural networks are simply particular cases of geometric algebra multidimensional neural networks and that some can be generated using support multivector machines.