Linear SVM Formulation

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

- Minimize

w.w

+ C (distance of error points to their correct zones)

- Add slack variable ੬i

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

Find 𝛼1,𝛼2,.....,𝛼m s.t

(no need to compute w explicitly)**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:

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