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1. Knowledge-Based Kernel Approximation Olvi Mangasarian, Jude Shavlik & Edward Wild
2. Basic Idea
3. Outline of Talk
4. Linear Kernel Approximation
5. Nonlinear Kernel Approximation
6. Linear Programming Formulation of Nonlinear Kernel Approximation
7. Gaussian Nonlinear Kernel
8. Prior Knowledge for Linear Kernel Approximation
9. Incorporating Knowledge Sets Into an SVM Classifier
10. Knowledge Set Equivalence Theorem
11. Proof of Equivalence Theorem Via Nonhomogeneous Farkas or LP Duality (x=At)
12. Knowledge-Based Constraints
13. Knowledge-Based SVM Approximation LP with Data and Knowledge Slacks
14. Three Numerical Examples Data Approximation Without & With Knowledge
15. Prior Knowledge for the sinc Function
16. sinc Function Approximation Without Prior Knowledge
17. sinc Function Approximation With Prior Knowledge
18. Two-Dimensional sinc Function
19. Data for Two-Dimensional sinc Function
20. Two-Dimensional Approximation Without Knowledge
21. Knowledge for Two-Dimensional sinc Function
22. Two-Dimensional Approximation With Knowledge
23. Two-Dimensional Hyperboloid Function
24. Data for Two-Dimensional Hyberboloid Function (Without Knowledge)
25. Data for Two-Dimensional Hyberboloid Function (Without Knowledge)
26. Two-Dimensional Hyperboloid Approximation Without Knowledge
27. Knowledge for Two-Dimensional Hyperboloid Function
28. Knowledge for Two-Dimensional Hyperboloid Function
29. Two-Dimensional Hyperboloid Approximation With Knowledge
30. Conclusion
31. Future Research
32. Web Pages
