An $\mathcal{O}(n\log n)$ projection operator for weighted $\ell_1$-norm regularization with sum constraint

TL;DR

This paper introduces a simple, efficient algorithm for projecting onto the weighted -norm ball with a sum constraint, improving computational efficiency for regularization tasks.

Contribution

It presents a novel (n  ) algorithm for weighted -norm projection with a sum constraint, along with an elementary proof of correctness.

Findings

Algorithm runs in (n  ) time complexity.

Implementation is publicly available for download.

Provides a straightforward proof of the projection method's validity.

Abstract

We provide a simple and efficient algorithm for the projection operator for weighted $\ell_1$-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded from the author's homepage.