Gaussian hyperplane rounding
= Gaussian hyperplane rounding
{c}
Given a real unit-vector <Gram matrix> $Y_{ij}=\langle v_i,v_j\rangle$, draw a <standard Gaussian random vector> $Z$ and set $y_i=\operatorname{sign}\langle v_i,Z\rangle$. Each coordinate is <almost surely> a sign; zero projections have <probability> zero. The same random separating hyperplane is used for every coordinate, so the signs need not be <independent>. Their pair expectations follow the <Gaussian sign-correlation identity>.