Lie Group Machine Learning 1st Edition by Fanzhang Li, Li Zhang, Zhao Zhang ISBN 311050068X 978-3110500684

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Product details: 

ISBN 10:  311050068X 

ISBN 13: 978-3110500684

Author: Fanzhang Li, Li Zhang, Zhao Zhang

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.

Table of contents: 

1. Lie Group Machine Learning
1.1 Introduction
1.2 Concepts of Lie Group Machine Learning
1.3 Algebraic Model of Lie Group Machine Learning
 1.3.1 Lie Algebras
 1.3.2 One-Parameter Subgroup
 1.3.3 Algebraic Model
1.4 Geometric Model of Lie Group Machine Learning
1.5 Axiom Hypothesis of Lie Group Machine Learning
1.6 Geometric Learning Algorithm for Dynkin Graphs in Lie Group Machine Learning
 1.6.1 Overview of Dynkin Graphs in Lie Group Machine Learning
 1.6.2 Classification Algorithm of Dynkin Diagrams in Lie Group Machine Learning
1.7 Linear Classifier Design of Lie Group Machine Learning
 1.7.1 Linear Classifier Design of Lie Group Machine Learning
 1.7.2 Lie Group Machine Learning SO(3) Classifier
 1.7.3 Classification of Text Based on Lie Group Machine Learning
1.8 Chapter Summary
Lie Group Subspace Orbit Generation Learning

2. Partial Order and Lattice in Lie Machine Learning (LML)
2.1 Basic Concepts of Partial Order and Lattice in LML
 2.1.1 Basic Concepts
 2.1.2 Partially Ordered Set in LML
 2.1.3 Möbius Function on Local Finite Partial Order in LML
 2.1.4 Gaussian Coefficients and Gaussian Polynomials in LML
 2.1.5 Lattices in LML
2.2 LML Subspace Orbit Generating Lattice Learning Algorithm
 2.2.1 LML Subspace Orbit Generation Lattice
2.3 Orbit Generation Learning Algorithm for LML Subspace
 2.3.1 Problem Description
 2.3.2 LML Learning Subspace Orbit Generation Lattice under the Action of the General Linear Group GLn(F)
 2.3.3 Learning Algorithms and Examples
2.4 Summary

3. Symplectic Group Learning
3.1 Symplectic Group Learning
3.2 Design of the Symplectic Group Classifier in Lie Group Machine Learning
 3.2.1 Problem Presentation
 3.2.2 Symplectic Group Classifier Description
 3.2.3 Design Method of Symplectic Group Classifier
 3.2.4 Symplectic Group Classifier Design for Face Recognition
 3.2.5 Symplectic Group Classifier Design for Data Set Classification
3.3 Symplectic Group Classifier Algorithm in Lie Group Machine Learning
 3.3.1 Symplectic Group Classifier Algorithm
 3.3.2 Verification of Symplectic Group Classifier Algorithm in Face Recognition
 3.3.3 Verification of Symplectic Group Classifier Algorithm in Data Set Classification
3.4 Application Example
 3.4.1 Processing of Images under Symplectic Matrix
 3.4.2 Instance Validation
3.5 Summary

4. Quantum Group Learning
4.1 Problem Presentation
4.2 Construction Method of Quantum Group Classifier in Lie Group Machine Learning
 4.2.1 Problem Description
 4.2.2 Construction of Quantum Group Classifier in Lie Group Machine Learning
 4.2.3 DNA Sequence Classification Based on Quantum Group Classifier
4.3 Application of Quantum Group Learning Algorithm in Molecular Docking
 4.3.1 Introduction to Molecular Docking Algorithm
 4.3.2 Molecular Docking Design Model Based on Quantum Group
 4.3.3 Molecular Matching Algorithm Based on Quantum Group Generators
 4.3.4 Molecular Docking Simulation Based on Quantum Group
 4.3.5 Experimental Results and Analysis
4.4 Summary

5. Lie Group Fibre Bundle Learning
5.1 Problem Presentation
5.2 Fibre Bundle Model
 5.2.1 Expression of Fibre Bundles in Manifold Learning
 5.2.2 Tangent Bundle Model for Manifold Learning
 5.2.3 Main Fibre Bundle Model
5.3 Fibre Bundle Learning Algorithm
 5.3.1 Vector Reduction Algorithm Based on Local Principal Direction of Tangent
 5.3.2 Main Link Curve Construction Algorithm Based on Tangent Contact
5.4 Summary

6. Lie Group Covering Learning
6.1 Theory of Lie Group Machine Learning Covering Algorithm
 6.1.1 Linear Representation of a Group
 6.1.2 Basic Properties of the Lie Group
6.2 Simply Connected Covering Algorithm of the Lie Group
 6.2.1 Research Status of Algorithm Based on Covering Idea
 6.2.2 Simply Connected Covering of Lie Group Machine Learning
 6.2.3 Algorithm Design
 6.2.4 Example Application Analysis
6.3 Multiply Connected Covering Algorithm of Lie Group Machine Learning
 6.3.1 LML Multiply Connected Covering Model
 6.3.2 Multiply Connected Covering Algorithm Design
 6.3.3 Applications
6.4 Application of the Covering Algorithm in Molecular Docking
 6.4.1 Introduction to the Molecular Docking Algorithm
 6.4.2 Mathematical Model and Evaluation Function of Molecular Docking
 6.4.3 Covering Strategy and Implementation of Molecular Docking
 6.4.4 Experimental Results and Analysis
6.5 Summary

7. Lie Group Deep Structure Learning
7.1 Introduction
7.2 Lie Group Deep Structure Learning
 7.2.1 Deep Structure Learning
 7.2.2 Construct Deep Structure Model
 7.2.3 Deep Structure Learning Algorithm
 7.2.4 Lie Group Deep Structure Learning Algorithm
 7.2.5 Experiment Analysis
7.3 Lie Group Layered Learning Algorithm
 7.3.1 Singular Value Feature Extraction
 7.3.2 Layered Learning Algorithm
 7.3.3 Experiment and Analysis
7.4 Lie Group Deep Structure Heuristic Learning
 7.4.1 Heuristic Learning Algorithm
 7.4.2 A* Algorithm
 7.4.3 Lie Group Deep Structure Heuristic Learning Algorithm
 7.4.4 Experiment and Analysis
7.5 Summary

8. Lie Group Semi-Supervised Learning
8.1 Introduction
 8.1.1 Research Status of Semi-Supervised Learning
 8.1.2 Questions Raised
8.2 Semi-Supervised Learning Model Based on the Lie Group
 8.2.1 Representation of the Lie Group in Semi-Supervised Study
 8.2.2 Semi-Supervised Learning Model Based on Lie Group Algebra Structure
 8.2.3 Semi-Supervised Learning Model Based on Geological Structure of the Lie Group
8.3 Semi-Supervised Learning Algorithm Based on a Linear Lie Group
 8.3.1 The General Linear Group
 8.3.2 Semi-Supervised Learning Algorithm Based on the Linear Lie Group
 8.3.3 Experiment
8.4 Semi-Supervised Learning Algorithm Based on Parameter Lie Group
 8.4.1 Sample Data Representation
 8.4.2 Semi-Supervised Learning Algorithm Based on Parameter Lie Group
 8.4.3 Experiment
8.5 Summary

9. Lie Group Kernel Learning
9.1 Matrix Group Learning Algorithm
 9.1.1 Related Basic Concepts
 9.1.2 Matrix Group
 9.1.3 Learning Algorithm of the Matrix Group
 9.1.4 Case Analysis
9.2 Gaussian Distribution on the Lie Group
 9.2.1 Gaussian Distribution of R+
 9.2.2 Gaussian Distribution of SO(2)
 9.2.3 Gaussian Distribution of SO(3)
9.3 Calculation of the Lie Group Inner Mean Value
9.4 Lie-Mean Learning Algorithm
 9.4.1 FLDA Algorithm
 9.4.2 Fisher Mapping in Lie Group Space
 9.4.3 Lie-Fisher Discriminant Analysis
9.5 Nuclear Learning Algorithm of the Lie Group
 9.5.1 Principle of the SVM Algorithm
 9.5.2 The Principle of KFDA
 9.5.3 Kernel
 9.5.4 Kernel of the Lie Group
 9.5.5 KLieDA Algorithm Based on the Lie Group Kernel Function
9.6 Case Application
 9.6.1 Experimental Analysis of the Lie-Fisher Algorithm
 9.6.2 Artificial Data Set
 9.6.3 Handwriting Recognition
 9.6.4 Covariance Lie Group Characteristic of the Lie-Fisher Handwriting Classification
9.7 Tensor Learning

10. Tensor Learning
10.1 Data Reduction Based on Tensor Methods
 10.1.1 GLRAM
 10.1.2 HAY
 10.1.3 2DPCA
 10.1.4 CubeSVD
 10.1.5 TSA
 10.1.6 Related Problem
10.2 Data Reduction Model Based on Tensor Fields
 10.2.1 Tensor Field on a Manifold
 10.2.2 Reduction Model Based on the Tensor Field
 10.2.3 Design of Data Reduction Algorithm Based on the Tensor Field
 10.2.4 Experiment
10.3 Learning Model and Algorithm Based on the Tensor Field
 10.3.1 Learning Model Based on the Tensor Field
 10.3.2 Tensor Bundle Learning Algorithm
 10.3.3 Classification Model Based on the Tensor Field
10.4 Classification Algorithm Based on the Tensor Field
Summary

11. Frame Bundle Connection Learning
11.1 Longitudinal Space Learning Model Based on Frame Bundle
11.2 Longitudinal Space Connection Learning Model Based on Frame Bundle
11.3 Horizontal Space Connection Learning Model Based on Frame Bundle
11.4 Related Applications
11.5 Summary

12. Spectral Estimation Learning
12.1 Concept and Definition of Spectral Estimation
 12.1.1 Research Background of the Spectral Estimation Method
 12.1.2 Concept and Definition of Spectral Estimation
 12.1.3 Research Progress in Learning Methods of Spectral Estimation
12.2 Relevant Theoretical Basis
 12.2.1 How to Construct a Similarity Matrix
 12.2.2 How to Choose the Appropriate Laplacian Matrix
 12.2.3 Selecting the Appropriate Feature Vector
 12.2.4 Determining the Number of Clusters
12.3 Synchronous Spectrum Estimation Learning Algorithm
 12.3.1 Graph Optimisation Criterion for Locally Preserving Mappings
 12.3.2 Asynchronous Spectrum Estimation Learning Model
 12.3.3 Synchronous Spectrum Estimation Learning Algorithm
 12.3.4 Case Verification
12.4 Theorems on Image Feature Manifolds
 12.4.1 The Comparison Principle of Image Feature Manifolds
 12.4.2 Topological Spherical Theorem
 12.4.3 Polarisation Theorem of Image Feature Manifolds
 12.4.4 Manifold Dimensionality Reduction Algorithm
12.5 Spectral Estimation Learning Algorithm for Topological Invariance of Image Feature Manifolds
 12.5.1 Algorithm and Analysis
 12.5.2 Example Analysis
12.6 Clustering Algorithm Based on the Topological Invariance Spectral Estimation of Image Feature Manifolds
12.7 Finsler Geometric Learning

13. Finsler Geometric Learning
13.1 Basic Concept
 13.1.1 Riemann Manifold
 13.1.2 Finsler Geometry
13.2 KNN Algorithm Based on the Finsler Metric
 13.2.1 K Nearest Neighbour Algorithm
 13.2.2 KNN Algorithm Based on the Finsler Metric
 13.2.3 Experimental Results and Analysis
13.3 Geometric Learning Algorithm Based on the Finsler Metric
 13.3.1 Supervised Manifold Learning Algorithm
 13.3.2 Finsler Geometric Learning Algorithm
13.4 Summary

14. Homology Boundary Learning
14.1 Boundary Learning Algorithm
 14.1.1 Tangent Vector Quantization (TVQ) Algorithm
 14.1.2 Regularised Large Marginal Classifier (RLMC)
 14.1.3 Boundary Detection Algorithm Based on the Boundary Markov Random Field and Boltzmann Machine
 14.1.4 Fuzzy Edge Detection Algorithm Based on the Qualification Function
14.2 Edge Division Method Based on Homological Algebra
 14.2.1 Basic Concepts of Homological Algebra
 14.2.2 Mapping of Homotopy and the Space of Homotopy
 14.2.3 Cohomology Edge Algorithm
 14.2.4 Cell Homology Edge Algorithm
14.3 Design and Analysis of Homology Edge Learning Algorithm
14.4 Summary

15. Category Representation Learning
15.1 Introduction
 15.1.1 Research Background
 15.1.2 Relation Between Category Theory and Computer Science
 15.1.3 Basic Concepts of Category Theory
 15.1.4 Proposed Problem
15.2 Category Representation of Learning Expressions
 15.2.1 Category Representation of Machine Learning Systems
 15.2.2 Category Representation of Learning Expressions
 15.2.3 Category Representation of the Learning Expression Functor
 15.2.4 Natural Transformation
15.3 Mapping Mechanism for Learning Expressions
 15.3.1 Abstract Concept of an Expression
 15.3.2 Mapping Mechanism Between Expressions
15.4 Classifier Design for Learning Expression Mapping Mechanism
 15.4.1 Classifier Algorithm
 15.4.2 Classifier Based on the Learning Expression Mapping Mechanism
 15.4.3 Example Analysis and Results
15.5 Example Analysis
 15.5.1 Instance Analysis of Learning Expression Mapping
 15.5.2 Case Analysis of Image Recognition
15.6 Summary

16. Neuromorphic Synergy Learning
16.1 Introduction
16.2 Core Scientific Problems
16.3 Lie Group Cognitive Theory Framework
16.4 Neuromorphic Synergy Learning Theoretical Framework
 16.4.1 Symbol Grounding Learning
 16.4.2 Bidirectional Synergy Learning
 16.4.3 Affordance Learning
 16.4.4 Multi-Scale Synergy Learning
16.5 Design of a Neuromorphic Synergy Learning Verification Platform
16.6 Summary

17. Appendix
17.1 Topological Group
17.2 Concept of Differential Geometry
17.3 Manifold Learning Algorithm
 17.3.1 Locallinear Embedding (LLE)
 17.3.2 Isometric Mapping (Isomap)
 17.3.3 Horizontal Linear Embedding (HLLE)
 17.3.4 Laplacian Eigenmap
 17.3.5 Local Tangency Space Arrangement (LTSA)
17.4 Basic Concept and Nature of Symplectic Group
17.5 Basic Concepts of Quantum Groups
 17.5.1 Image Description of the Quantum Group
 17.5.2 Definition and Decision Algorithm of Quantum Group
 17.5.3 Quantisation
 17.5.4 Representation of Quantum Groups
17.6 Fibre Bundle

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Tags: Fanzhang Li, Li Zhang, Zhao Zhang, Lie Group, Machine Learning