Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks
Guilherme Vieira, Marcos Eduardo Valle
TL;DR
This work tackles automated ALL detection from blood smear images by extending convolutional neural networks to HvCNNs defined over eight four‑dimensional associative hypercomplex algebras, including $A[-1,-1]$ (quaternions), $A[-1,+1]$ (coquaternions), and $B[-1,+1]$ (tessarines). It demonstrates that HSV-encoded inputs combined with non‑quaternion algebras yield the strongest performance, with HvCNNs achieving around $96$–$97\%$ median accuracy on ALL-IDB2 while using only about $3.6\times 10^{4}$ parameters, far fewer than a ResNet18 baseline. The authors also provide an emulation method to implement HvCNNs within standard real-valued DL libraries and show that coquaternions and tessarines can outperform quaternions on HSV data, contributing to efficient CAD for leukemia. Overall, the paper introduces a principled hypercomplex framework and empirically validates its effectiveness for color-sensitive medical image classification.
Abstract
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.