$$\begin{array}{ll} \text{minimize} & f(X)= \| X-M||_F^2 \\ \text{subject to} & \sigma_{k+1}(X) \le a \end{array}$$
where $X\in R^{n \times m}$ is the matrix;
$\sigma_{k+1}(X)$ is the $(k+1)^{th}$ largest sigular value of $X$ .
$a$ is just some constant e.g., a = 0.5; $M\in R^{n \times m}$ is the data matrix also constant.
It there any efficient algorithm (even rough approximation) to solve this problem? Thanks