Regularization method for reduced biquaternion neural network

A reduced biquaternion neural network (RQNN) has achieved significant success in machine learning. However, as the reduced biquaternion algebra system contains infinite zero divisors, the RQNN can be easily trapped in a local minimum and overfitting. In this paper, we propose a new regularization scheme for the RQNN to address these issues. Firstly, we propose a new operation in the reduced biquaternion domain named the reduced biquaternion complex modulus (RQCM), which can extract the scale transformation of reduced biquaternions and decrease the unreasonable network constraints caused by constrained phases. Secondly, we mathematically analyse the properties of the reduced biquaternions and obtain the geometric meaning of the RQCM. Finally, we propose an improved weight decay method using the RQCM which can better project the reduced biquaternion in terms of the scale and phase. In addition, our proposed method can effectively solve the non-differentiability of reduced biquaternion matrix and overfitting problem in the process of network parameter updating. The experimental results demonstrate that the proposed method is effective in color image classification and denoising taskas, and outperforms the state of the arts.