Quaternion MLP Neural Networks Based on the Maximum Correntropy Criterion

TL;DR

This paper introduces a novel quaternion MLP neural network training algorithm based on the maximum correntropy criterion, utilizing split quaternion activation and a new quaternion operator, with simulations confirming its feasibility.

Contribution

It develops a gradient ascent algorithm for quaternion MLPs based on MCC, incorporating a split quaternion activation function and a new quaternion operator, extending MSE algorithms to MCC.

Findings

Feasibility demonstrated through simulations

Effective quaternion MLP training with MCC

Extension from MSE to MCC algorithm

Abstract

We propose a gradient ascent algorithm for quaternion multilayer perceptron (MLP) networks based on the cost function of the maximum correntropy criterion (MCC). In the algorithm, we use the split quaternion activation function based on the generalized Hamilton-real quaternion gradient. By introducing a new quaternion operator, we first rewrite the early quaternion single layer perceptron algorithm. Secondly, we propose a gradient descent algorithm for quaternion multilayer perceptron based on the cost function of the mean square error (MSE). Finally, the MSE algorithm is extended to the MCC algorithm. Simulations show the feasibility of the proposed method.