Clifford Convolutional Neural Networks: Concepts, Implementation, and an Application for Lymphoblast Image Classification

This chapter presents the basic concepts of convolutional neural network (CNN) models on Clifford algebras, referred to as Clifford CNNs. The basic building blocks, such as dense and convolutional layers, are briefly addressed. Besides the mathematical formulation, this chapter describes how to implement Clifford CNNs using standard deep-learning libraries. It also presents an application of Clifford CNNs to a medical image classification task, namely the diagnosis of acute lymphoblastic leukemia (ALL). ALL is a type of cancer in the bloodstream characterized by malformed lymphocytes called lymphoblasts. The image classification task aims to discriminate healthy cells from lymphoblasts. Corroborating with previous results reported in the literature, Clifford CNNs outperform real-valued networks of equivalent size in this application. Precisely, the real-valued and a Clifford CNN achieved an average accuracy of 94.60% and 97.02%, respectively. Moreover, we present smaller versions of Clifford CNNs with roughly 75% fewer parameters, yielding a 96.50% average accuracy. The results reported in this work are comparable to high-end models in the literature despite having several orders of magnitude fewer parameters.