On processing three dimensional data by quaternionic neural networks

The performance of layered neural networks with quaternionic encoding variables are investigated in this paper. The form of local analyticity with Wirtinger representation is adopted for a backpropagation learning algorithm in this network. A quaternionic version of tanh function is used for the activation function in neuron states´ updates. As tasks of the performance evaluation of the presented networks, two types of three dimensional data processing problem are used; the prediction of the Lorentz attractor and affine transformations in three dimensional space.