Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application

TL;DR

This paper presents a straightforward and efficient algorithm for projecting points onto the probability simplex, along with a simple proof and an application in clustering.

Contribution

It introduces a new, elementary proof of an existing algorithm and demonstrates its application in Laplacian K-modes clustering.

Findings

Algorithm is efficient and easy to implement

Proof is simple and accessible

Application improves clustering performance

Abstract

We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.