Projection onto the capped simplex
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and C++ implementations of the proposed algorithm can be downloaded at https://eng.ucmerced.edu/people/wwang5.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Fast Projection onto the Capped Simplex with Applications to Sparse Regression in Bioinformatics
We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm bas…
CPUregressionProjection onto the probability simplex: An efficient algorithm with a simple proof, and an application
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.
ClusteringSparse projections onto the simplex
Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from …
Density EstimationRankmax: An Adaptive Projection Alternative to the Softmax Function
Several machine learning models involve mapping a score vector to a probability vector. Usually, this is done by projecting the score vector onto a probability simplex, and such projections are often characterized as Lip…
Convex optimization over a probability simplex
We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the pos…