Linear SVM Formulation
Limitations of previous SVM formulation
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
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
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:
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