Knowledge-Based Kernel Approximation

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 TheoremVia Nonhomogeneous Farkas or LP Duality (x=A�t)

12. Knowledge-Based Constraints

13. Knowledge-Based SVM ApproximationLP with Data and Knowledge Slacks

14. Three Numerical ExamplesData 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