1. Intelligent Numerical Computation1 Center:Width:

2. Intelligent Numerical Computation2 Radial basis function network

3. Intelligent Numerical Computation3 Find an interpolation function with N RBFs

4. Intelligent Numerical Computation4 Or Solve

5. Intelligent Numerical Computation5 A class of RBFs

6. Intelligent Numerical Computation6 Generalization to multi-dimensional target Interpolation conditions Interpolation function

7. Intelligent Numerical Computation7 M<<N Adapted by an algorithm A bias

8. Intelligent Numerical Computation8 A RBF network Or in matrix

9. Intelligent Numerical Computation9 Universal approximation

10. Intelligent Numerical Computation10 Extended basis functions

11. Intelligent Numerical Computation11 where

12. Intelligent Numerical Computation12 Minimize the cost function

13. Intelligent Numerical Computation13

14. Intelligent Numerical Computation14 I

15. Intelligent Numerical Computation15 Advanced clustering algorithms II LVQ III K-means algorithm IV Kohonen self-organizing algorithm

16. Intelligent Numerical Computation16 to where

17. Intelligent Numerical Computation17 Assignment #3 Implement a training algorithm for a RBF network Multi-dimensional input space One-dimensional output space You can select supervised training or two-stage training or more advanced training algorithm Your program should be able to read a training file and a testing file to evaluate performance. The last column of the training file will be the desired output.

18. Intelligent Numerical Computation18 Variants

19. Intelligent Numerical Computation19 Model size vs generalization Minimal model size and maximal generalization

20. Intelligent Numerical Computation20 Applications http://lib.stat.cmu.edu/datasets/ http://www.cs.toronto.edu/~delve/data/datasets.html http://www.phys.uni.torun.pl/neural/node12.html Radial basis function interpolation for 3-D ultrasound http://svr-www.eng.cam.ac.uk/~ahg/rnr20/publications.html