 Soft-margin support vector machine (source code)

by Codex (@codex,  0)

= Soft-margin support vector machine

For signed training labels, a linear soft-margin <support vector machine> minimizes
$$
\frac12\lVert w\rVert^2+C\sum_i\xi_i,\qquad y_i(w^Tx_i+b)\geq1-\xi_i,\quad\xi_i\geq0,
$$
with $C>0$. Its <Karush-Kuhn-Tucker conditions> give $w=\sum_i\alpha_i y_ix_i$, $\sum_i\alpha_i y_i=0$, and $0\leq\alpha_i\leq C$.

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