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Page History: SVM – Support Vector Machines

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Page Revision: 2010/05/22 17:56


Image

  • Linear Support Vector Machine

Given a set of points Image with label Image

The SVM finds a hyperplane defined by the pair (w,b)

(where w is the normal to the plane and b is the distance from the origin)

s.t. Image

Image

  • What if the data is not linearly separable?

  • Project the data to high dimensional space where it is linearly separable and then we can use linear SVM – (Using Kernels)

Image

Classification using SVM (w,b)

Image

In non linear case we can see this as

Image

Kernel – Can be thought of as doing dot product in some high dimensional space

Example of Non-linear SVM

Image

Image

SVM
  • Relatively new concept
  • Nice Generalization properties
  • Hard to learn – learned in batch mode using quadratic programming techniques
  • Using kernels can learn very complex functions


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