Quaternionic Multilayer Perceptron with Local Analyticity

Abstract

A multi-layered perceptron type neural network is presented and analyzed in this paper. All neuronal parameters such as input, output, action potential and connection weight are encoded by quaternions, which are a class of hypercomplex number system. Local analytic condition is imposed on the activation function in updating neurons’ states in order to construct learning algorithm for this network. An error back-propagation algorithm is introduced for modifying the connection weights of the network.

Keywords

• quaternion
• local analyticity
• Wirtinger calculus
• multilayer perceptron
• error back-propagation