A framework to generate sparsity-inducing regularizers for enhanced
low-rank matrix completion
Abstract
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.