Review of Clifford algebra-based AI methods in signal analysis

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'.

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Publication Details

Journal
Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
Published
2026-08-13
DOI
https://doi.org/10.1098/rsta.2025.0099
Citations
1
Primary Topic
Algebraic and Geometric Analysis
Type
article
Field-Weighted Citation Impact
15.11
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article

Review of Clifford algebra-based AI methods in signal analysis

Petr Vašík, Roman Byrtus, Francesco Prinzi, Salvatore Vitabile
1 citations
Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
Algebraic and Geometric Analysis
15.11
article

Review of Clifford algebra-based AI methods in signal analysis

Petr Vašík, Roman Byrtus, Francesco Prinzi, Salvatore Vitabile
article en
1 citations

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'.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering SciencesVol. 384(2326)
Brno University of Technology (CZ), University of Palermo (IT)
Openalex Percentile: Top 1%
Algebraic and Geometric Analysis
15.11
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