Decreasing Weighted Sorted $\ell_1$ Regularization

Xiangrong Zeng; Mário A. T. Figueiredo

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arXiv · 1404.3184

Decreasing Weighted Sorted $\ell_1$ Regularization

Xiangrong Zeng·Mário A. T. Figueiredo

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Abstract

We consider a new family of regularizers, termed {\it weighted sorted $\ell_1$ norms} (WSL1), which generalizes the recently introduced {\it octagonal shrinkage and clustering algorithm for regression} (OSCAR) and also contains the $\ell_1$ and $\ell_{\infty}$ norms as particular instances. We focus on a special case of the WSL1, the {\sl decreasing WSL1} (DWSL1), where the elements of the argument vector are sorted in non-increasing order and the weights are also non-increasing. In this paper, after showing that the DWSL1 is indeed a norm, we derive two key tools for its use as a regularizer: the dual norm and the Moreau proximity operator.

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BibTeX RIS

Xiangrong Zeng, Mário A. T. Figueiredo. 2014-04-11. Decreasing Weighted Sorted $\ell_1$ Regularization. https://arxiv.org/abs/1404.3184

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