Matrix tensor factorisation

Question

Say we have a matrix $A$ expressed as the tensor $$A=\sum_{m=1}^Mx^{(m)}A^{(m)}$$ where $A$ and $A^{(i)}$ are $N\times P$ matrices and $x$ is a $M\times 1$ vector. I would like to decompose $A$ (or some approximation of it) as a product of three matrices $U_{N\times Q}V_{Q\times Q}W_{Q\times P}$ (it resembles SVD a bit). I think I might have seen this somewhere but I can't recall exactly how to do it. Thank you.