Title: Structured low-rank matrix learning: algorithms and applications,
Abstract: We consider the problem of learning a low-rank matrix, constrained to lie in
a linear subspace, and introduce a novel factorization for modeling such
matrices. A salient feature of the proposed factorization scheme is it
decouples the low-rank and the structural constraints onto separate factors. We
formulate the optimization problem on the Riemannian spectrahedron manifold,
where the Riemannian framework allows to develop computationally efficient
conjugate gradient and trust-region algorithms. Experiments on problems such as
standard/robust/non-negative matrix completion, Hankel matrix learning and
multi-task learning demonstrate the efficacy of our approach. A shorter version
of this work has been published in ICML'18.