= Support vector
{title2=$\alpha_i>0$}
{wiki}
In a <support vector machine>, a dual support vector is a training observation with positive dual coefficient $\alpha_i>0$. Such an observation appears in the fitted score $f(x)=\sum_i\alpha_i y_i k(x_i,x)+b$, where $k$ is the <positive-definite kernel>.
For a <soft-margin support vector machine>, the <Karush-Kuhn-Tucker conditions> imply that every dual support vector has signed margin $y_if(x_i)\leq1$. The converse can fail at equality: a point exactly on a margin boundary may have $\alpha_i=0$ in a degenerate solution. Points strictly inside the margin have $\alpha_i=C$ in the usual linear-slack formulation. Some texts instead use a geometric convention counting all observations on or inside the margin. The <dual support vectors and margin degeneracy> distinction matters for <support-vector leave-one-out error bounds>.
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