Hypercomplex-Valued Convolutional Neural Networks

Hypercomplex numbers generalize the notion of complex and hyperbolic numbers as well as quaternions, tessarines, octonions, and many other high-dimensional algebras including Clifford and Cayley-Dickson algebras. This repository contains the source codes and examples of hypercomplex-valued convolutional neural networks (HvCNNs), which include quaternionic models as particular instances.

See examples in the following Jupyter notebook files:

Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

This Jupyter notebook contains the hypercomplex-valued convolutional neural networks used for acute lymphoblastic leukemia detection, as described in the paper with the same title by Guilherme Vieira and Marcos Eduardo Valle accepted for presentation at the 2022 International Joint Conference on Neural Networks (IJCNN 2022), as part of the World Congress on Computational Intelligence (WCCI 2022). The notebook uses the ALL-IDB2 dataset, a public and free dataset of microscopic images of blood samples designed for the evaluation and the comparison of algorithms for segmentation and image classification. Further information on the ALL-IDB dataset can be found at https://homes.di.unimi.it/scotti/all/

Authors:

• Marcos Eduardo Valle and Guilherme Vieira - University of Campinas

Clifford Convolutional Neural Networks for Lymphoblast Image Classification (ICACGA 2022)

This Jupyter notebook contains the hypercomplex-valued convolutional neural networks used for acute lymphoblastic leukemia detection, as described in the paper with the same title by Guilherme Vieira, Marcos Eduardo Valle and Wilder Lopes, accepted for presentation at the 2022 International Conference of Advanced Computational Applications of Geometric Algebra (ICACGA 2022). The convolutional neural networks considered in this notebook have fewer parameters than the models considered in the previous notebook. The reduced number of parameters are achived by reducing the number of filters and increasing the number of layers (deep). The notebook uses the ALL-IDB2 dataset, a public and free dataset of microscopic images of blood samples designed for the evaluation and the comparison of algorithms for segmentation and image classification. Further information on the ALL-IDB dataset can be found at https://homes.di.unimi.it/scotti/all/

Authors:

• Marcos Eduardo Valle and Guilherme Vieira - University of Campinas
• Wilder Lopes - Ogarantia