  This paper features convolutional neural networks defined on hypercomplex
algebras applied to classify lymphocytes in blood smear digital microscopic
images. Such classification is helpful for the diagnosis of acute lymphoblast
leukemia (ALL), a type of blood cancer. We perform the classification task
using eight hypercomplex-valued convolutional neural networks (HvCNNs) along
with real-valued convolutional networks. Our results show that HvCNNs perform
better than the real-valued model, showcasing higher accuracy with a much
smaller number of parameters. Moreover, we found that HvCNNs based on Clifford
algebras processing HSV-encoded images attained the highest observed
accuracies. Precisely, our HvCNN yielded an average accuracy rate of 96.6%
using the ALL-IDB2 dataset with a 50% train-test split, a value extremely close
to the state-of-the-art models but using a much simpler architecture with
significantly fewer parameters.
