Collaborative filtering algorithms such as matrix factorization techniques are recently gaining momentum due to their promising performance on recommender systems. However, most collaborative filtering algorithms suffer from data sparsity. Active learning algorithms are effective in reducing the sparsity problem for recommender systems by requesting users to give ratings to some items when they enter the systems. In this paper, a new matrix factorization model, called Enhanced SVD (ESVD) is proposed, which incorporates the classic matrix factorization algorithms with ratings completion inspired by active learning. In addition, the connection between the prediction accuracy and the density of matrix is built to further explore its potentials. We also propose the Multi-layer ESVD (MESVD), which learns the model iteratively to further improve the prediction accuracy. To handle the imbalanced datasets that contain far more users than items or more items than users, the Item-wise ESVD (IESVD) and User-wise ESVD (UESVD) are presented, respectively. The proposed methods are evaluated on the famous Netflix and Movielens datasets. Experimental results validate their effectiveness in terms of both accuracy and efficiency when compared with traditional matrix factorization methods and active learning methods.