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"Intrinsic Metrics and Mutual Information: From Abstract Measurements to Machine Learning"
Chapter 1: Introduction
Motivation for the book
Overview of the key concepts: intrinsic metrics, mutual information, nonlinear tensor algebra, etc.
Chapter 2: Intrinsic Metrics and Differential Geometry
Review of differential geometry and intrinsic metrics
The relationship between intrinsic metrics and nonlinear tensor algebra
Applications of intrinsic metrics in machine learning
Chapter 3: Mutual Information and Information Theory
Overview of information theory and mutual information
Calculation of mutual information for nonlinear systems
Applications of mutual information in feature selection and clustering
Chapter 4: Nonlinear Tensor Algebra and Kernel Methods
Overview of nonlinear tensor algebra
Application of kernel methods to nonlinear tensor algebra
Use of kernel functions to define the measure of linear dependency between feature vectors in a nonlinear space
Chapter 5: From Abstract Measurements to Emergent Features
Use of mutual information as an abstract foundation for emergent features
Development of machine learning experiments that rely on abstract bits containing information about system states
Analysis of the resulting emergent concepts of comparison, distance, order, etc.
Chapter 6: Applications of Intrinsic Metrics and Mutual Information in Machine Learning
Case studies of using intrinsic metrics and mutual information in machine learning tasks
Comparison with traditional machine learning techniques
Future directions and potential limitations of the approach
Chapter 7: Conclusion
Summary of key points
Implications of the approach for the field of machine learning and beyond
Suggestions for further reading and research