Let $X \in \mathbb{R}^{n\times N}$ be a given matrix. I want to solve the following optimization problem
\begin{align} \min_{A\in \mathbb{R}^{m\times n}} \frac{1}{N^2}\|(AX)^T(AX)-T\|_F^2 \\ \text{s.t}\quad A_{mn}\in \{0,1\}, \end{align}
i.e, $A$ is a binary matrix. Is there any method or algorithm to solve this kind of problem? I just need some hints and/or references. Thank you.