Lie Group Machine Learning

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. * Focuses on machining learning theoretical frameworks based on Lie group theory. * Combines algorithms with project experiences. * An introductory reference for AI researchers and engineers. 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.-- Source other than Library of Congress Cover 1 Lie Group Machine Learning 5 © 2019 6 Preface 7 Contents 11 1 Lie group machine learning model 19 2 Lie group subspace orbit generation learning 57 3 Symplectic group learning 99 4 Quantum group learning 141 5 Lie group fibre bundle learning 165 6 Lie group covering learning 183 7 Lie group deep structure learning 225 8 Lie group semi–supervised learning 253 9 Lie group kernel learning 293 10 Tensor learning 337 11 Frame bundle connection learning 365 12 Spectral estimation learning 375 13 Finsler geometric learning 401 14 Homology boundary learning 419 15 Category representation learning 433 16 Neuromorphic synergy learning 483 17 Appendix 503 Authors 531 Index 533 Back Cover 537

This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. It further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, the book is a self-contained introductory for computer scientists and engineers.