Systems, Patterns and Data Engineering with Geometric Calculi

This collection aims to overview the essentials of geometric calculus (GC) formalism, report on state-of-the-art applications, and explore its implications for deep learning. It includes contributions from experts in robotics, molecular geometry, medical imaging, orientation measurements, contact elements, and computational methodologies. The book is intended for a wide range of research profiles, particularly those interested in bridging GC with applications in deep neural networks.

Format: Paperback / softback
Length: 179 pages
Publication date: 18 July 2022
Publisher: Springer Nature Switzerland AG

The aim of this collection aligns perfectly with the objectives of the homonymous mini-symposium (MS) held at ICIAM-2019, which sought to provide an overview of the fundamental principles of geometric calculus (GC) formalism, showcase its remarkable applications, and explore how GC can contribute to innovative approaches in deep learning. The first three contributions, which correspond to lectures delivered at the MS, offer insightful perspectives on recent advancements in the application of GC in the fields of robotics, molecular geometry, and medical imaging. The subsequent three, particularly invited contributions, delve into enhancing the expressiveness of GC in orientation measurements across various metrics, the treatment of contact elements, and the exploration of efficient computational methodologies. The final two contributions, also delivered as lectures at the MS, address two key aspects of deep learning. Firstly, a concrete quaternionic convolutional neural network layer for image classification is presented, showcasing contrast invariance and highlighting its potential for addressing challenging image recognition tasks. Secondly, a comprehensive overview of automatic learning is provided, aimed at guiding the development of neural networks whose units process elements from suitable algebraic structures, such as geometric algebra.

This book, in essence, falls within the domain of mathematical engineering and is designed to cater to a diverse range of research profiles. Specifically, it aims to inspire and provide guidance to individuals seeking materials and problems that bridge GC with applications of utmost current interest, particularly in the flourishing field of GC-based deep neural networks. By presenting a comprehensive collection of research papers, this book serves as a valuable resource for scholars, researchers, and practitioners in the field of mathematics, computer science, and engineering.

Weight: 302g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030744885
Edition number: 1st ed. 2021