On Learning Matrices with Orthogonal Columns or Disjoint Supports
Abstract
We investigate new matrix penalties to jointly learn linear models with orthogonality constraints, generalizing the work of Xiao et al. [24] who proposed a strictly convex matrix norm for orthogonal transfer. We show that this norm converges to a particular atomic norm when its convexity parameter decreases, leading to new algorithmic solutions to minimize it. We also investigate concave formulations of this norm, corresponding to more aggressive strategies to induce orthogonality, and show how these penalties can also be used to learn sparse models with disjoint supports.
Cite
Text
Vervier et al. "On Learning Matrices with Orthogonal Columns or Disjoint Supports." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014. doi:10.1007/978-3-662-44845-8_18Markdown
[Vervier et al. "On Learning Matrices with Orthogonal Columns or Disjoint Supports." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014.](https://mlanthology.org/ecmlpkdd/2014/vervier2014ecmlpkdd-learning/) doi:10.1007/978-3-662-44845-8_18BibTeX
@inproceedings{vervier2014ecmlpkdd-learning,
title = {{On Learning Matrices with Orthogonal Columns or Disjoint Supports}},
author = {Vervier, Kevin and Mahé, Pierre and d'Aspremont, Alexandre and Veyrieras, Jean-Baptiste and Vert, Jean-Philippe},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2014},
pages = {274-289},
doi = {10.1007/978-3-662-44845-8_18},
url = {https://mlanthology.org/ecmlpkdd/2014/vervier2014ecmlpkdd-learning/}
}