1. Kernel Properties 2012 Computer Science PhD Showcase 17 February 2012 Roberto Valerio Dr. Ricardo Vilalta Pattern Analysis Lab

2. Kernel Properties Agenda • Introduction • Objective • Current work • Experiments • Conclusions • Publications

3. Introduction • Machine Learning • What is it? • Kernel methods • What are kernel methods?

4. Support Vector Machine • Constructs a hyper plane in a high dimensional space with the largest margin.

5. Support Vector Machine

6. Kernel Trick • Avoid explicit mapping of the infinite dimensional space • By using this mapping we avoid dealing with a high dimensional space and we can find a separating hyper plane with the kernel matrix

7. Which kernel?

8. Objective • Analyze the behaviors of different kernels to generate properties that allow us to determine the optimal kernel.

9. Current Work • Kernel Matrices evaluations • Behavioral evaluation of the Kernel transformation in varied data density situations • Identifying key points in the hyper plane construction and kernel mappings

10. Experiments Toy Data sets Bayes Error Non Linear Non linear and Bayes error

11. Experiments LinearKernelMatrix Bayes Error Non Linear Non linear and Bayes error

12. Experiments Polynomial Kernel Degree 4 Kernel Bayes Error Non Linear Non linear and Bayes error

13. Experiments Linear Kernel Density Evaluation Bayes Error Non Linear Non linear and Bayes error

14. Experiments Polynomial Kernel Degree 4 Density evaluation Bayes Error Non Linear Non linear and Bayes error

15. Experiments

16. Conclusions • Each kernel has its own pattern • We can take advantage of these patterns to generate more accurate classifications.

17. Future work • Identify the relationship between the kernel pattern and the misclassification error • Use this relationship to select the optimal kernel or as a guideline to construct new kernels.

18. Publications Classification of Sources of Ionizing Radiation in Space Missions: A Machine Learning Approach. Vilalta, R., Kuchibhotla, S., Hoang, S., Valerio, R., Ocegueda, F., and Pinsky, L., (2012) ActaFutura, 5, pp.111-119, 2012. Development of Pattern Recognition Software for Tracks of Ionizing Radiation in Medipix2-Based (TimePix) Pixel Detector Devices. Vilalta R., Valerio R., Kuchibhotla S., Pinsky L. (2010) 18th International Conference on Computing in High Energy and Nuclear Physics (CHEP-10), Taipei, Taiwan. Journal of Physics: Conference Series. The Effect of the Fragmentation Problem in Decision Tree Learning Applied to the Search for Single Top Quark Production. Vilalta R., Valerio R., Ocegueda-Hernandez F., Watts G. (2009)17th International Conference on Computing in High Energy and Nuclear Physics (CHEP-09), Prague, Czech Republic. Journal of Physics: Conference Series.