Book 1 of the Geometric Series

Geometric Methods

Computational Modeling

A volume in the Geometric Series by Andrew H. Bond.

Contents

Part I: Foundations

  1. Chapter 1: Why Geometry?
  2. Chapter 2: Mahalanobis Distance and Weighted Metric Spaces
  3. Chapter 3: Hyperbolic Geometry for Hierarchical Data
  4. Chapter 4: SPD Manifolds and Spectral Geometry
  5. Chapter 5: Topological Data Analysis

Part II: Algorithms on Manifolds

  1. Chapter 6: Pathfinding on Manifolds
  2. Chapter 7: Equilibrium on Manifolds
  3. Chapter 8: Pareto Optimization
  4. Chapter 9: Adversarial Robustness and the Model Robustness Index
  5. Chapter 10: Adversarial Probing

Part III: Design Patterns

  1. Chapter 11: The Subset Enumeration Pattern
  2. Chapter 12: Compositional Testing
  3. Chapter 13: Group-Theoretic Data Augmentation
  4. Chapter 14: Gradient Reversal and Invariance Training
  5. Chapter 15: Cholesky Parameterization for Positive-Definiteness

Part IV: Systems & Integration

  1. Chapter 16: Building Geometric Pipelines
  2. Chapter 17: Scaling to High-Dimensional Spaces
  3. Chapter 18: Deploying Geometric Validation in Production
  4. Chapter 19: Case Study --- Software Defect Prediction
  5. Chapter 20: Case Study --- Cetacean Bioacoustics

Appendices

  1. Appendix A: Mathematical Notation and Conventions
  2. Appendix B: Software Dependencies and Installation
  3. Appendix C: Selected Proofs and Derivations