Review of Clifford algebra-based AI methods in signal analysis

Abstract

Hypercomplex number systems, such as complex numbers and quaternions, have found many uses in the area of signal analysis. Clifford algebras, along with the embedding of (usually) a real vector space, can be used to represent some of the commonly used hypercomplex algebras through subalgebras. Concepts used in hypercomplex algebras can be easily further extended to Clifford algebra. An overview of methods along with their advantages and disadvantages based on Clifford algebra, mostly used in signal analysis, is given in this review, with a focus on applications in neural networks. The use of the described methods is discussed in the context of medical imaging.

This article is part of the theme issue ‘Modern applications of geometric algebra’.