# Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2205.13273 · HTML: https://mlsanity.com/paper/2205.13273/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [A General Framework for Hypercomplex-valued Extreme Learning Machines](https://mlsanity.com/paper/2101.06166/) (2021)
- [Applications of Clifford's Geometric Algebra](https://mlsanity.com/paper/1305.5663/) (2013)
- [Quaternion-Valued Recurrent Projection Neural Networks on Unit Quaternions](https://mlsanity.com/paper/2001.11846/) (2020)
- [Quaternion-Valued Convolutional Neural Network Applied for Acute Lymphoblastic Leukemia Diagnosis](https://mlsanity.com/paper/2112.06685/) (2021)

## Built on by (most cited first, 8 of 8)

- [Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2401.02277/) (2024)
- [Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2209.02456/) (2022)
- [Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2309.07716/) (2023)
- [Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling](https://mlsanity.com/paper/2310.07623/) (2023)
- [Quaternion Convolutional Neural Networks: Current Advances and Future Directions](https://mlsanity.com/paper/2307.08663/) (2023)
- [Hypercomplex neural network in time series forecasting of stock data](https://mlsanity.com/paper/2401.04632/) (2024)
- [Selected aspects of complex, hypercomplex and fuzzy neural networks](https://mlsanity.com/paper/2301.00007/) (2022)
- [V-EfficientNets: Vector-Valued Efficiently Scaled Convolutional Neural Network Models](https://mlsanity.com/paper/2505.05659/) (2025)

## Abstract (arXiv)

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.