A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion
This work addresses a specific bottleneck in matrix completion for researchers in optimization and machine learning, offering incremental improvements in regularization techniques.
The authors tackled the problem of generating sparsity-inducing regularizers for low-rank matrix completion by developing a framework that produces such regularizers with closed-form proximity operators, and their methods demonstrated effectiveness in recovery performance and runtime in numerical tests.
Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.