10/28/2009
1
Support Vector Machines
Outline
•
Transform a linear learner into a non
‐
linear
learner
•
Kernels can make high
‐
dimensional spaces
tractable
•
Kernels can make non
‐
vectorial data tractable
Non
‐
Linear Problems
Problem:
•
some tasks have non
‐
linear structure
•
no hyperplane is sufficiently accurate
How can SVMs learn non
‐
linear classification rules?
Extending the Hypothesis Space
Idea: add more features
Learn linear rule in feature space.
Example:
The separating hyperplane in feature space is
degree two polynomial in input space.
Transformation
•
Instead of
x
1
, x
2
use

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10/28/2009
2
How do we find these features?
•
F(
x) =
Reminder
From http://www.support
‐
vector.net/icml
‐
tutorial.pdf
Reminder
From http://www.support
‐
vector.net/icml
‐
tutorial.pdf
Observation
From http://www.support
‐
vector.net/icml
‐
tutorial.pdf