Neurocomputing with High Dimensional Parameters - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 41

The processing of high-dimensional data is an important task for artificial neural
networks. Multilayered neural networks of different class of high-dimensional para-
meters are presented and analyzed in this topic. All neuronal parameters such as
input, output, action potential, and connection weights are encoded by respective
high-dimensional number system. The computational capability of a single complex-
valued, vector-valued, or quaternionic-valued neuron has been independently pre-
sented. In order to construct learning algorithm for respective networks analytic,
local analytic, or non-analytic conditions may be imposed on the activation function
in updating neuron's states. Instead of using conventional description, i.e., cartesian
representation, the Cliff-Ford algebra, Vector Calculus, and Wirtinger calculus may
be adopted to standardize the learning rules of high dimensional neural networks.
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