A Unified Framework for Structured Low-rank Matrix Learning

Pratik Jawanpuria, Bamdev Mishra
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:2254-2263, 2018.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-jawanpuria18a, title = {A Unified Framework for Structured Low-rank Matrix Learning}, author = {Jawanpuria, Pratik and Mishra, Bamdev}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {2254--2263}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/jawanpuria18a/jawanpuria18a.pdf}, url = {https://proceedings.mlr.press/v80/jawanpuria18a.html}, 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.} }
Endnote
%0 Conference Paper %T A Unified Framework for Structured Low-rank Matrix Learning %A Pratik Jawanpuria %A Bamdev Mishra %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-jawanpuria18a %I PMLR %P 2254--2263 %U https://proceedings.mlr.press/v80/jawanpuria18a.html %V 80 %X 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.
APA
Jawanpuria, P. & Mishra, B.. (2018). A Unified Framework for Structured Low-rank Matrix Learning. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:2254-2263 Available from https://proceedings.mlr.press/v80/jawanpuria18a.html.

Related Material