Table of Content:Chapter 1 Introduction1.1 Introduction1.2 Basic concepts in Lie group machine learning1.3 Aaxiom and hypothesis1.4 Model1.5 Dynkin diagram and geometric algorithm1.6 Classifier designChapter 2 Covering learning in Lie group machine learning2.1 Algorithms and theories2.2 Single-connected covering learning algorithm2.3 Multiply-connected covering learning algorithm2.4 Applications of covering algorithm in molecular docking2.5 SummaryChapter 3 Deep learning and structure3.1 Introduction3.2 Deep learning3.3 Layer-by-layer learning algorithm3.4 Heuristic deep learning algorithm3.5 SummaryChapter 4 Lie group semi-supervised learning4.1 Introduction4.2 Semi-supervised learning model based on Lie group4.3 Semi-supervised learning algorithm based on linear Lie group4.4 Semi-supervised learning algorithm based on nonlinear Lie group4.5 SummaryChapter 5 Lie group nuclear Learning5.1 Matrix group learning and algorithm5.2 Gauss distribution in Lie group5.3 Calculation of mean value in Lie group5.4 Learning algorithm based on Lie group mean5.5 Nuclear learning and algorithm5.6 Applications and case studies5.7 SummaryChapter 6 Tensor learning6.1 Data reduction based on tensor6.2 Data reduction model based on tensor field6.3 Model and algorithm design based on tensor field6.4 SummaryChapter 7 Connection learning based on frame bundle7.1 Vertical spatial learning model based on frame bundle7.2 Vertical spatial connection learning model based on frame bundle7.3 Horizontal spatial learning model based on frame bundle7.4 Horizontal and vertical special algorithms based on frame bundle7.5 SummaryChapter 8 Spectrum estimation learning8.1 Concepts and definitions in spectral estimation8.2 Theoretical foundations8.3 Synchronous spectrum estimation learning algorithm8.4 Comparison of image features manifold8.5 Spectrum estimation learning algorithm with topological invariant image feature manifolds8.6 Clustering algorithm with topological invariant image feature manifolds8.7 SummaryChapter 9 Finsler geometry learning9.1 Basic concepts9.2 KNN algorithm based on Finsler metric9.3 Geometric learning algorithm based Finsler metrics9.4 SummaryChapter 10 Homology boundary learning10.1 Boundary learning algorithm10.2 Boundary partitioning based on homology algebra10.3 Design and analysis for homology boundary learning algorithm10.4 SummaryChapter 11 Learning based on prototype theory11.1 Introduction11.2 Prototype representation for learning expression11.3 Mapping for the learning expression11.4 Classifier design for the mapping for learning expression11.5 Case Study11.6 SummaryReferences