A Scalable and Feasible Matrix Completion Approach Using Random Projection

The low rank matrix completion problem has attracted great attention and been widely studied in collaborative filtering and recommendation systems. The rank minimization problem is NP-hard, so the problem is usually relaxed into a matrix nuclear norm minimization. However, the usage is limited in scability due to the high computational complexity of singular value decomposition (SVD). In this paper we introduce a random projection to handle this limitation. In particular, we use a randomized SVD to accelerate the classical Soft-Impute algorithm for the matrix completion problem. The empirical results show that our approach is more efficient while achieving almost same performance.

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