Lie Group Machine Learning

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Lie Group Machine Learning

Fanzhang Li,Li Zhang,Zhao Zhang
Lie Group Machine Learning Book PDF

Author : Fanzhang Li,Li Zhang,Zhao Zhang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 533 pages
File Size : 53,6 Mb
Release : 2018-11-05
Category : Computers
ISBN : 9783110499506

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Lie Group Machine Learning by Fanzhang Li,Li Zhang,Zhao Zhang Pdf

This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.

Mathematics for Machine Learning

Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Mathematics for Machine Learning Book PDF

Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Publisher : Cambridge University Press
Page : 391 pages
File Size : 51,5 Mb
Release : 2020-04-23
Category : Computers
ISBN : 9781108470049

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Mathematics for Machine Learning by Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong Pdf

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

Geometric Structures of Statistical Physics, Information Geometry, and Learning

Frédéric Barbaresco,Frank Nielsen
Geometric Structures of Statistical Physics Information Geometry and Learning Book PDF

Author : Frédéric Barbaresco,Frank Nielsen
Publisher : Springer Nature
Page : 466 pages
File Size : 49,8 Mb
Release : 2021-06-27
Category : Mathematics
ISBN : 9783030779573

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Geometric Structures of Statistical Physics, Information Geometry, and Learning by Frédéric Barbaresco,Frank Nielsen Pdf

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.

Differential Geometry and Lie Groups

Jean Gallier,Jocelyn Quaintance
Differential Geometry and Lie Groups Book PDF

Author : Jean Gallier,Jocelyn Quaintance
Publisher : Springer Nature
Page : 777 pages
File Size : 50,9 Mb
Release : 2020-08-14
Category : Mathematics
ISBN : 9783030460402

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Differential Geometry and Lie Groups by Jean Gallier,Jocelyn Quaintance Pdf

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.

Understanding Machine Learning

Shai Shalev-Shwartz,Shai Ben-David
Understanding Machine Learning Book PDF

Author : Shai Shalev-Shwartz,Shai Ben-David
Publisher : Cambridge University Press
Page : 415 pages
File Size : 48,8 Mb
Release : 2014-05-19
Category : Computers
ISBN : 9781107057135

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Understanding Machine Learning by Shai Shalev-Shwartz,Shai Ben-David Pdf

Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

An Introduction to Lie Groups and Lie Algebras

Alexander A. Kirillov
An Introduction to Lie Groups and Lie Algebras Book PDF

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 45,7 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Artificial Neural Networks and Machine Learning – ICANN 2023

Lazaros Iliadis,Antonios Papaleonidas,Plamen Angelov,Chrisina Jayne
Artificial Neural Networks and Machine Learning ICANN 2023 Book PDF

Author : Lazaros Iliadis,Antonios Papaleonidas,Plamen Angelov,Chrisina Jayne
Publisher : Springer Nature
Page : 623 pages
File Size : 48,9 Mb
Release : 2023-10-23
Category : Computers
ISBN : 9783031442070

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Artificial Neural Networks and Machine Learning – ICANN 2023 by Lazaros Iliadis,Antonios Papaleonidas,Plamen Angelov,Chrisina Jayne Pdf

The 10-volume set LNCS 14254-14263 constitutes the proceedings of the 32nd International Conference on Artificial Neural Networks and Machine Learning, ICANN 2023, which took place in Heraklion, Crete, Greece, during September 26–29, 2023. The 426 full papers, 9 short papers and 9 abstract papers included in these proceedings were carefully reviewed and selected from 947 submissions. ICANN is a dual-track conference, featuring tracks in brain inspired computing on the one hand, and machine learning on the other, with strong cross-disciplinary interactions and applications.

Geometric Science of Information

Frank Nielsen,Frédéric Barbaresco
Geometric Science of Information Book PDF

Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer
Page : 764 pages
File Size : 44,9 Mb
Release : 2019-08-19
Category : Computers
ISBN : 9783030269807

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Geometric Science of Information by Frank Nielsen,Frédéric Barbaresco Pdf

This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 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.

Geometry and Statistics

Anonim
Geometry and Statistics Book PDF

Author : Anonim
Publisher : Academic Press
Page : 490 pages
File Size : 51,8 Mb
Release : 2022-07-15
Category : Mathematics
ISBN : 9780323913461

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Geometry and Statistics by Anonim Pdf

Geometry and Statistics, Volume 46 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Geometry and Statistics

Deep Learning

Ian Goodfellow,Yoshua Bengio,Aaron Courville
Deep Learning Book PDF

Author : Ian Goodfellow,Yoshua Bengio,Aaron Courville
Publisher : MIT Press
Page : 801 pages
File Size : 54,5 Mb
Release : 2016-11-10
Category : Computers
ISBN : 9780262337373

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Deep Learning by Ian Goodfellow,Yoshua Bengio,Aaron Courville Pdf

An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Differential Geometry and Lie Groups

Jean Gallier,Jocelyn Quaintance
Differential Geometry and Lie Groups Book PDF

Author : Jean Gallier,Jocelyn Quaintance
Publisher : Springer Nature
Page : 627 pages
File Size : 42,8 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9783030460471

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Differential Geometry and Lie Groups by Jean Gallier,Jocelyn Quaintance Pdf

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.

Progress in Information Geometry

Frank Nielsen
Progress in Information Geometry Book PDF

Author : Frank Nielsen
Publisher : Springer Nature
Page : 274 pages
File Size : 53,5 Mb
Release : 2021-03-14
Category : Science
ISBN : 9783030654597

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Progress in Information Geometry by Frank Nielsen Pdf

This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).

Lifelong Machine Learning, Second Edition

Zhiyuan Sun,Bing Leno da Silva
Lifelong Machine Learning Second Edition Book PDF

Author : Zhiyuan Sun,Bing Leno da Silva
Publisher : Springer Nature
Page : 187 pages
File Size : 44,8 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031015816

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Lifelong Machine Learning, Second Edition by Zhiyuan Sun,Bing Leno da Silva Pdf

Lifelong Machine Learning, Second Edition is an introduction to an advanced machine learning paradigm that continuously learns by accumulating past knowledge that it then uses in future learning and problem solving. In contrast, the current dominant machine learning paradigm learns in isolation: given a training dataset, it runs a machine learning algorithm on the dataset to produce a model that is then used in its intended application. It makes no attempt to retain the learned knowledge and use it in subsequent learning. Unlike this isolated system, humans learn effectively with only a few examples precisely because our learning is very knowledge-driven: the knowledge learned in the past helps us learn new things with little data or effort. Lifelong learning aims to emulate this capability, because without it, an AI system cannot be considered truly intelligent. Research in lifelong learning has developed significantly in the relatively short time since the first edition of this book was published. The purpose of this second edition is to expand the definition of lifelong learning, update the content of several chapters, and add a new chapter about continual learning in deep neural networks—which has been actively researched over the past two or three years. A few chapters have also been reorganized to make each of them more coherent for the reader. Moreover, the authors want to propose a unified framework for the research area. Currently, there are several research topics in machine learning that are closely related to lifelong learning—most notably, multi-task learning, transfer learning, and meta-learning—because they also employ the idea of knowledge sharing and transfer. This book brings all these topics under one roof and discusses their similarities and differences. Its goal is to introduce this emerging machine learning paradigm and present a comprehensive survey and review of the important research results and latest ideas in the area. This book is thus suitable for students, researchers, and practitioners who are interested in machine learning, data mining, natural language processing, or pattern recognition. Lecturers can readily use the book for courses in any of these related fields.

Joseph Fourier 250th Birthday

Frédéric Barbaresco,Jean-Pierre Gazeau
Joseph Fourier 250th Birthday Book PDF

Author : Frédéric Barbaresco,Jean-Pierre Gazeau
Publisher : MDPI
Page : 260 pages
File Size : 51,9 Mb
Release : 2019-03-28
Category : Science
ISBN : 9783038977469

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Joseph Fourier 250th Birthday by Frédéric Barbaresco,Jean-Pierre Gazeau Pdf

For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Frontiers In Entropy Across The Disciplines - Panorama Of Entropy: Theory, Computation, And Applications

M Zuhair Nashed,Willi Freeden
Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications Book PDF

Author : M Zuhair Nashed,Willi Freeden
Publisher : World Scientific
Page : 757 pages
File Size : 48,5 Mb
Release : 2022-08-30
Category : Science
ISBN : 9789811259418

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Frontiers In Entropy Across The Disciplines - Panorama Of Entropy: Theory, Computation, And Applications by M Zuhair Nashed,Willi Freeden Pdf

Frontiers in Entropy Across the Disciplines presents a panorama of entropy emphasizing mathematical theory, physical and scientific significance, computational methods, and applications in mathematics, physics, statistics, engineering, biomedical signals, and signal processing.In the last century classical concepts of entropy were introduced in the areas of thermodynamics, information theory, probability theory, statistics, dynamical systems, and ergodic theory. During the past 50 years, dozens of new concepts of entropy have been introduced and studied in many disciplines. This volume captures significant developments in this arena. It features expository, review, and research papers by distinguished mathematicians and scientists from many disciplines. The level of mathematics ranges from intermediate level to research level. Each chapter contains a comprehensive list of references. Topics include entropy and society, entropy and time, Souriau entropy on symplectic model of statistical physics, new definitions of entropy, geometric theory of heat and information, maximum entropy in Bayesian networks, maximum entropy methods, entropy analysis of biomedical signals (review and comparison of methods), spectral entropy and its application to video coding and speech coding, a comprehensive review of 50 years of entropy in dynamics, a comprehensive review on entropy, entropy-like quantities and applications, topological entropy of multimodal maps, entropy production in complex systems, entropy production and convergence to equilibrium, reversibility and irreversibility in entropy, nonequilibrium entropy, index of various entropy, entropy and the greatest blunder ever.