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This paper presents a new method for calculating the low-rank approximation of a highly incomplete trajectory matrix for subspace video stabilization. We extend moving factorization proposed in [1], which is a streamable method based on least squares. By utilizing sparse representation of trajectories, the proposed factorization method is more accurate while still streamable. We test our sparse moving factorization on synthetic data as well as real videos. Experiments on synthetic sequence demonstrate the numerical properties of our method, and stabilized videos show that our method outperforms moving factorization for subspace video stabilization. In addition, our results are also better than the ones from some other state-of-the-art video stabilization methods.