Abstract Tuning hyper-parameters for large-scale matrix factorization (MF) is very time consuming and sometimes unacceptable. Intuitively, we want to tune hyper-parameters on small sub-matrix sample and then exploit them into the original large-scale matrix. However, most of existing MF methods are scale-variant, which means the optimal hyperparameters usually change with the different scale of matrices. To this end, in this paper we propose a scale-invariant parametric MF method, where a set of scale-invariant parameters is defined for model complexity regularization. Therefore, the proposed method can free us from tuning hyper-parameters on large-scale matrix, and achieve a good performance in a more efficient way. Extensive experiments on real-world dataset clearly validate both the effectiveness and efficiency of our method.