In the context of the profound integration of big data and artificial intelligence, matrix completion stands as a pivotal technology within machine learning and data mining. It finds widespread application across domains such as recommendation systems, computer vision, and social network analysis. Traditional approaches predominantly hinge on the low-rank properties of matrices, yet they fall short in harnessing the latent graph-structured information inherent in the data.

The research team led by Professor Wang Yao and Associate Professor Wang Kaidong from the School of Management at Xi’an Jiaotong University has introduced a non-convex optimization algorithm termed GSGD (Graph-regularized Scaled Gradient Descent). This innovative algorithm facilitates the efficient recovery of missing data by integrating graph-structured information. Built upon a preconditioned projected gradient descent framework, the algorithm offers robust theoretical guarantees for a linear convergence rate and near-optimal sample complexity.

Experimental results indicate that GSGD surpasses existing mainstream methods in terms of recovery accuracy, computational efficiency, and resilience to noisy edges. It exhibits substantial advantages in scenarios such as recommendation systems and social networks. The research findings have been published in the INFORMS Journal on Computing, a premier journal in the field of operations research and management science. This advancement provides an effective tool for data processing and analysis in the big data era, fostering the practical application of artificial intelligence technologies.