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Kernel Properties2012 Computer Science PhD Showcase
17 February 2012
Roberto Valerio
Dr. Ricardo Vilalta
Pattern Analysis Lab
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Kernel Properties
Agenda• Introduction• Objective• Current work• Experiments• Conclusions• Publications
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Introduction
• Machine Learning– What is it?
• Kernel methods– What are kernel methods?
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Support Vector Machine
• Constructs a hyper plane in a high dimensional space with the largest margin.
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Support Vector Machine
?
Feature 1
Feature 2
.
.
Feature n
Infinite Dimensional
Space
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
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
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Which kernel?
Linear Polynomial Gaussian Hyperbolic ?
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.
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
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Experiments
Toy Data sets
Bayes Error Non Linear Non linear and Bayes error
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Experiments
Linear Kernel Matrix
Bayes Error Non Linear Non linear and Bayes error
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Experiments
Polynomial Kernel Degree 4 Kernel
Bayes Error Non Linear Non linear and Bayes error
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Experiments
Linear Kernel Density Evaluation
Bayes Error Non Linear Non linear and Bayes error
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Experiments
Polynomial Kernel Degree 4 Density evaluation
Bayes Error Non Linear Non linear and Bayes error
Kernel Properties – Roberto Valerio 2012 Computer Science PhD Showcase -17 February 2012
Experiments
Linear
Poly 2
Poly 3
Poly 4
RBF 0.5
RBF 0.25
95
95.3
94.3
90.5
95.1
95
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
Accuracy Results
NonLinear Overlap Non Linear Bayes Error
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.
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.
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.
