Nonconvex matrix completion with Nesterov’s acceleration

Abstract

Background: In matrix completion fields, the traditional convex regularization may fall short of delivering reliable low-rank estimators with good prediction performance. Previous works use the alternation least squares algorithm to optimize the nonconvex regularization. However, this algorithm has high time complexities and requires more iterations to reach convergence, which cannot scale to large-scale matrix completion problems. We need to develop faster algorithm to examine large amount of data to uncover the correlations between items for the big data analytics. Results: In this work, we adopt the randomized SVD decomposition and Nesterov's momentum to accelerate the optimization of nonconvex matrix completion. The experimental results on four real world recommendation system datasets show that the proposed algorithm achieves tremendous speed increases whilst maintaining comparable performance with the alternating least squares (ALS) method for nonconvex (convex) matrix completions. Conclusions: Our novel algorithm can achieve comparable performance with previous algorithms but with shorter running time.

A parameterized three-operator splitting algorithm for non-convex minimization problems with applications

“…First, we perform singular value decomposition (SVD) [10,35,36] on the image, resulting in a low-rank image I r . We then select a set Ω of m entries uniformly at random from all possible entries, with a sampling ratio of p = m 493×517 .…”