This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.

Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.

This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.

This Festschrift volume, published in honour of J. Ian Munro, contains contributions written by some of his colleagues, former students, and friends. In celebration of his 66th birthday the colloquium "Conference on Space Efficient Data Structures, Streams and Algorithms" was held in Waterloo, ON, Canada, during August 15-16, 2013. The articles presented herein cover some of the main topics of Ian's research interests. Together they give a good overall perspective of the last 40 years of research in algorithms and data structures.

Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

The three volume set LNCS 8834, LNCS 8835, and LNCS 8836 constitutes the proceedings of the 20th International Conference on Neural Information Processing, ICONIP 2014, held in Kuching, Malaysia, in November 2014. The 231 full papers presented were carefully reviewed and selected from 375 submissions. The selected papers cover major topics of theoretical research, empirical study, and applications of neural information processing research. The 3 volumes represent topical sections containing articles on cognitive science, neural networks and learning systems, theory and design, applications, kernel and statistical methods, evolutionary computation and hybrid intelligent systems, signal and image processing, and special sessions intelligent systems for supporting decision, making processes,theories and applications, cognitive robotics, and learning systems for social network and web mining.

This book offers a detailed and comprehensive analysis of multi-aspect data learning, focusing especially on representation learning approaches for unsupervised machine learning. It covers state-of-the-art representation learning techniques for clustering and their applications in various domains. This is the first book to systematically review multi-aspect data learning, incorporating a range of concepts and applications. Additionally, it is the first to comprehensively investigate manifold learning for dimensionality reduction in multi-view data learning. The book presents the latest advances in matrix factorization, subspace clustering, spectral clustering and deep learning methods, with a particular emphasis on the challenges and characteristics of multi-aspect data. Each chapter includes a thorough discussion of state-of-the-art of multi-aspect data learning methods and important research gaps. The book provides readers with the necessary foundational knowledge to apply these methods to new domains and applications, as well as inspire new research in this emerging field.

Lavishly illustrated in color, this textbook takes an applied approach to introduce undergraduate students to the basic principles of structural geology. The book provides unique links to industry applications in the upper crust, including petroleum and groundwater geology, which highlight the importance of structural geology in exploration and exploitation of petroleum and water resources. Topics range from faults and fractures forming near the surface to shear zones and folds of the deep crust. Students are engaged through examples and parallels drawn from practical everyday situations, enabling them to connect theory with practice. Containing numerous end-of-chapter problems, e-learning modules, and with stunning field photos and illustrations, this book provides the ultimate learning experience for all students of structural geology.