A stochastic alternating minimization approach for large scale Low Rank Matrix Factorization

Low Rank Matrix Factorization (LRMF) is a classical problem that arises in a wide range of practical contexts, especially in collaborative filtering, dimension reduction, etc. In this paper, a stochastic alternating minimization approach applied to LRMF problem is proposed. The main idea of the approach is to randomly sample partial rows of the matrix to perform parameter update during training using alternating minimization, which not only reduces the computational requirements but also declines the over-fitting risk. The simulation results on synthetic datasets show that both alternating minimization-based algorithm and the proposed stochastic variant are applicable for LRMF task, while the proposed algorithm is more competitive for large-scale datasets due to its low-complexity and scalability.