A Unified Framework for Structured Lowrank Matrix Learning
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:22542263, 2018.
Abstract
We consider the problem of learning a lowrank 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 lowrank 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 trustregion algorithms. Experiments on problems such as standard/robust/nonnegative matrix completion, Hankel matrix learning and multitask learning demonstrate the efficacy of our approach.
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