  The problem of recovering a low-rank matrix from the linear constraints,
known as affine matrix rank minimization problem, has been attracting extensive
attention in recent years. In general, affine matrix rank minimization problem
is a NP-hard. In our latest work, a non-convex fraction function is studied to
approximate the rank function in affine matrix rank minimization problem and
translate the NP-hard affine matrix rank minimization problem into a
transformed affine matrix rank minimization problem. A scheme of iterative
singular value thresholding algorithm is generated to solve the regularized
transformed affine matrix rank minimization problem. However, one of the
drawbacks for our iterative singular value thresholding algorithm is that the
parameter $a$, which influences the behaviour of non-convex fraction function
in the regularized transformed affine matrix rank minimization problem, needs
to be determined manually in every simulation. In fact, how to determine the
optimal parameter $a$ is not an easy problem. Here instead, in this paper, we
will generate an adaptive iterative singular value thresholding algorithm to
solve the regularized transformed affine matrix rank minimization problem. When
doing so, our new algorithm will be intelligent both for the choice of the
regularized parameter $\lambda$ and the parameter $a$.
