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SVM: Maximum Margin with Noise in Machine Learning

Linear SVM Formulation
 
Limitations of previous SVM formulation


  • What if the data is not linearly separable?
  • Or noisy data points?

Extend the definition of maximum margin to allow no-separating planes.

Objective to be minimized

- Minimize
   w.w
   + C (distance of error points to their correct zones)
- Add slack variable ੬i

Maximum Margin with Noise


Lagrangian

 𝛼i's and 𝛽i's are Lagrange multipliers (≥ 0).

Dual Formulation

Find 𝛼1,𝛼2,.....,𝛼m   s.t




Solution to Soft Margin Classification

  • xi with non-zero 𝛼i will be support vectors.
  • Solution to the dual problem is:
(no need to compute w explicitly)

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