Geometric Methods in Computational Modeling

Andrew H. Bond — San José State University

20
Chapters
4
Parts
3
Appendices
10k+
Lines

Part I: Foundations

  • 1. Why Geometry?
  • 2. Mahalanobis Distance & Weighted Metrics
  • 3. Hyperbolic Geometry for Hierarchical Data
  • 4. SPD Manifolds & Spectral Geometry
  • 5. Topological Data Analysis

Part II: Algorithms on Manifolds

  • 6. Pathfinding on Manifolds
  • 7. Equilibrium on Manifolds
  • 8. Pareto Optimization
  • 9. Adversarial Robustness & MRI
  • 10. Adversarial Probing

Part III: Design Patterns

  • 11. Subset Enumeration
  • 12. Compositional Testing
  • 13. Group-Theoretic Augmentation
  • 14. Gradient Reversal & Invariance
  • 15. Cholesky Parameterization

Part IV: Systems & Integration

  • 16. Building Geometric Pipelines
  • 17. Scaling to High Dimensions
  • 18. Production Deployment
  • 19. Case Study: Defect Prediction
  • 20. Case Study: Bioacoustics