Neural networks in the Clifford domain

Georgiou and Koutsougeras (1992) and Gordon et al. (1990) extended the traditional multi-layer perceptron to allow activation, threshold and weight values to take on complex values instead of real values. Although at first sight this might seem biologically unmotivated, if phase as well as frequency information in synaptic pulse trains plays a part in processing in the brain, then complex valued networks could be used to model phase information, in the same way as complex numbers are used to model phase in electrical engineering. Clifford algebras offer a higher dimensional generalization of the complex numbers. The present authors have shown that it is possible to derive a back error propagation algorithm for networks with Clifford valued weight and activation values. This work ceases to be biologically motivated, but it is hoped that by bringing together multidimensional signals into single elements of a Clifford algebra, that more compact representations of the pattern space will be obtained