  The field of neural networks has seen significant advances in recent years
with the development of deep and convolutional neural networks. Although many
of the current works address real-valued models, recent studies reveal that
neural networks with hypercomplex-valued parameters can better capture,
generalize, and represent the complexity of multidimensional data. This paper
explores the quaternion-valued convolutional neural network application for a
pattern recognition task from medicine, namely, the diagnosis of acute
lymphoblastic leukemia. Precisely, we compare the performance of real-valued
and quaternion-valued convolutional neural networks to classify lymphoblasts
from the peripheral blood smear microscopic images. The quaternion-valued
convolutional neural network achieved better or similar performance than its
corresponding real-valued network but using only 34% of its parameters. This
result confirms that quaternion algebra allows capturing and extracting
information from a color image with fewer parameters.
