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

2. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Kernel Properties Agenda Introduction Objective Current work Experiments Conclusions Publications

3. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Introduction Machine Learning –What is it? Kernel methods –What are kernel methods?

4. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Support Vector Machine

5. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Support Vector Machine ? Feature 1 Feature 2.. Feature n Infinite Dimensional Space

6. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Kernel Trick

7. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Which kernel? Linear Polynomial Gaussian Hyperbolic ?

8. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Objective Analyze the behaviors of different kernels to generate properties that allow us to determine the optimal kernel.

9. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 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. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Experiments Toy Data sets Bayes ErrorNon LinearNon linear and Bayes error

11. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Experiments Linear Kernel Matrix Bayes ErrorNon LinearNon linear and Bayes error

12. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Experiments Polynomial Kernel Degree 4 Kernel Bayes ErrorNon LinearNon linear and Bayes error

13. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Experiments Linear Kernel Density Evaluation Bayes ErrorNon LinearNon linear and Bayes error

14. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Experiments Polynomial Kernel Degree 4 Density evaluation Bayes ErrorNon LinearNon linear and Bayes error

15. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Experiments

16. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 Conclusions Each kernel has its own pattern We can take advantage of these patterns to generate more accurate classifications.

17. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 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. Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase  17 February 2012 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) Acta Futura, 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.