An $O(n\log(n))$ Algorithm for Projecting Onto the Ordered Weighted $\ell_1$ Norm Ball
Optimization and Control
2015-06-29 v3 Machine Learning
Abstract
The ordered weighted (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform simultaneous clustering and regression. In this paper, we show how to compute the projection of an -dimensional vector onto the OWL norm ball in operations. In addition, we illustrate the performance of our algorithm on a synthetic regression test.
Cite
@article{arxiv.1505.00870,
title = {An $O(n\log(n))$ Algorithm for Projecting Onto the Ordered Weighted $\ell_1$ Norm Ball},
author = {Damek Davis},
journal= {arXiv preprint arXiv:1505.00870},
year = {2015}
}
Comments
1 Figures, 1 table, 14 pages, Example added to appendix