  We develop an efficient stochastic variance reduced gradient descent
algorithm to solve the affine rank minimization problem consists of finding a
matrix of minimum rank from linear measurements. The proposed algorithm as a
stochastic gradient descent strategy enjoys a more favorable complexity than
full gradients. It also reduces the variance of the stochastic gradient at each
iteration and accelerate the rate of convergence. We prove that the proposed
algorithm converges linearly in expectation to the solution under a restricted
isometry condition. The numerical experiments show that the proposed algorithm
has a clearly advantageous balance of efficiency, adaptivity, and accuracy
compared with other state-of-the-art greedy algorithms.
