Figure 4

Computation of P _knn ( y =1|x) . Two weak classifiers are available: $h_{{\mathrm{a}}_1}$ and $h_{{\mathrm{a}}_2}$. Applying these weak classifiers on a training database gives the set of points ${\mathcal{\mathscr{H}}}_{\mathrm{a}}$ (the red circles are positive points and the blue squares are negative points). Given an unknown sample x, $h_{{\mathrm{a}}_1}\left(\mathrm{x}\right)$ and $h_{{\mathrm{a}}_2}\left(\mathrm{x}\right)$ are computed and the k nearest neighbors of $\left(h_{{\mathrm{a}}_1}\right(\mathrm{x}),h_{{\mathrm{a}}_2}(\mathrm{x}\left)\right)$ are searched in ${\mathcal{\mathscr{H}}}_{\mathrm{a}}$. In the figure, k=3, and the nearest neighbors are two positive points and one negative point which leads to P _knn(y=1|x)=2/3.