Overview
- Integrated perspective of mathematical engineering based on geometric calculi
- A comprehensive formalism for deep neural networks based on geometric algebras
- Coverage of relevant algorithms, particularly for automatic learning, and of advanced computational aspects
Part of the book series: SEMA SIMAI Springer Series (SEMA SIMAI, volume 13)
Part of the book sub series: ICIAM 2019 SEMA SIMAI Springer Series (ICIAM2019SSSS)
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Table of contents (8 papers)
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Front Matter
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Back Matter
Keywords
About this book
The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra.
The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.
Editors and Affiliations
About the editor
Bibliographic Information
Book Title: Systems, Patterns and Data Engineering with Geometric Calculi
Editors: Sebastià Xambó-Descamps
Series Title: SEMA SIMAI Springer Series
DOI: https://doi.org/10.1007/978-3-030-74486-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-74485-4Published: 17 July 2021
Softcover ISBN: 978-3-030-74488-5Published: 18 July 2022
eBook ISBN: 978-3-030-74486-1Published: 16 July 2021
Series ISSN: 2199-3041
Series E-ISSN: 2199-305X
Edition Number: 1
Number of Pages: IX, 179
Number of Illustrations: 26 b/w illustrations, 38 illustrations in colour
Topics: Applications of Mathematics, Mathematical Applications in Computer Science, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Math. Applications in Chemistry