  Since their first applications, Convolutional Neural Networks (CNNs) have
solved problems that have advanced the state-of-the-art in several domains.
CNNs represent information using real numbers. Despite encouraging results,
theoretical analysis shows that representations such as hyper-complex numbers
can achieve richer representational capacities than real numbers, and that
Hamilton products can capture intrinsic interchannel relationships. Moreover,
in the last few years, experimental research has shown that Quaternion-Valued
CNNs (QCNNs) can achieve similar performance with fewer parameters than their
real-valued counterparts. This paper condenses research in the development of
QCNNs from its very beginnings. We propose a conceptual organization of current
trends and analyze the main building blocks used in the design of QCNN models.
Based on this conceptual organization, we propose future directions of
research.
