\begin{equation}\label{eq:maxcorr}
   \rho_k= \max_{\tilde{a}_k\in\mathbb{R}^p\,\text{, }  \tilde{b}_k\in\mathbb{R}^q} \text{corr}(\langle \tilde{a}_k,Y \rangle \langle \tilde{b}_k,X\rangle),
\end{equation}
