 Soft-margin support vector machine

ID: soft-margin-support-vector-machine

For signed training labels, a linear soft-margin support vector machine minimizes

\frac{1}{2} ∥ w ∥^{2} + C \sum_{i} ξ_{i}, y_{i} (w^{T} x_{i} + b) \geq 1 - ξ_{i}, ξ_{i} \geq 0,

with

C > 0

w = \sum_{i} α_{i} y_{i} x_{i}

\sum_{i} α_{i} y_{i} = 0

, and

0 \leq α_{i} \leq C

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