LRSVRG-IMC: An SVRG-Based Algorithm for LowRank Inductive Matrix Completion
This addresses a bottleneck in IoT data completion and recommendation systems, offering an incremental improvement for nonconvex optimization in matrix completion.
The paper tackles the problem of saddle points and slow convergence in low-rank inductive matrix completion by proposing LRSVRG-IMC, a stochastic variance reduction gradient-based algorithm that achieves linear convergence and near-optimal sample complexity, as verified on synthetic datasets.
Low-rank inductive matrix completion (IMC) is currently widely used in IoT data completion, recommendation systems, and so on, as the side information in IMC has demonstrated great potential in reducing sample point remains a major obstacle for the convergence of the nonconvex solutions to IMC. What's more, carefully choosing the initial solution alone does not usually help remove the saddle points. To address this problem, we propose a stocastic variance reduction gradient-based algorithm called LRSVRG-IMC. LRSVRG-IMC can escape from the saddle points under various low-rank and sparse conditions with a properly chosen initial input. We also prove that LRSVVRG-IMC achieves both a linear convergence rate and a near-optimal sample complexity. The superiority and applicability of LRSVRG-IMC are verified via experiments on synthetic datasets.