Constructing Convolutional Neural Networks Based on Quaternion

A convolutional neural network based on quaternion, a four-dimensional hypercomplex number system, is proposed and evaluated in this paper. Called Quaternionic Convolutional Neural Networks (QCNNs), these networks can accept and operate three-dimensional signals by neurons in the networks. The performances of the proposed networks are investigated through classification of CIFAR-10 color images, and it is shown that the proposed QCNN outperforms a conventional (real-valued) CNN.