Title: Alternating Iteratively Reweighted Minimization Algorithms for Low-Rank Matrix Factorization,
Abstract: Nowadays, the availability of large-scale data in disparate application
domains urges the deployment of sophisticated tools for extracting valuable
knowledge out of this huge bulk of information. In that vein, low-rank
representations (LRRs) which seek low-dimensional embeddings of data have
naturally appeared. In an effort to reduce computational complexity and improve
estimation performance, LRR has been viewed via a matrix factorization (MF)
perspective. Recently, low-rank MF (LRMF) approaches have been proposed for
tackling the inherent weakness of MF i.e., the unawareness of the dimension of
the low-dimensional space where data reside. Herein, inspired by the merits of
iterative reweighted schemes for rank minimization, we come up with a generic
low-rank promoting regularization function. Then, focusing on a specific
instance of it, we propose a regularizer that imposes column-sparsity jointly
on the two matrix factors that result from MF, thus promoting low-rankness on
the optimization problem. The problems of denoising, matrix completion and
non-negative matrix factorization (NMF) are redefined according to the new LRMF
formulation and solved via efficient Newton-type algorithms with proven
theoretical guarantees as to their convergence and rates of convergence to
stationary points. The effectiveness of the proposed algorithms is verified in
diverse simulated and real data experiments.