Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application
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Abstract (arXiv)
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.
Key facts. Cited by 65 papers in the map (data through 13 Oct 2026). First posted on arXiv 6 Sep 2013.
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Citing papers per year: 2021: 10; 2022: 7; 2023: 16; 2024: 9; 2025: 12; 2026: 11.
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50 most cited of 65 All 65 (JSON)
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- 2026Constrained Multi-Objective Reinforcement Learning with Max-Min Criterion29 May 2026
- 2026Locally Coherent, Globally Incoherent: Bounding Compositional Incoherence in Multi-Component LLM Agents28 May 2026
- 2026Polyhedral Unmixing: Bridging Semantic Segmentation with Hyperspectral Unmixing via Polyhedral-Cone Partitioning31 Mar 2026
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- 2025Many-to-Many Matching via Sparsity Controlled Optimal Transport31 Mar 2025
- 2025Towards Optimal Offline Reinforcement Learning15 Mar 2025
- 2025Balanced Rate-Distortion Optimization in Learned Image Compression27 Feb 2025
- 2025Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoning13 Jan 2025
- 2024Two Models for Surface Segmentation using the Total Variation of the Normal Vector30 Nov 2024
- 2024Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension26 Nov 2024
- 2024Unsupervised Feature Selection Algorithm Based on Graph Filtering and Self-representation1 Nov 2024
- 2024Bypass Back-propagation: Optimization-based Structural Pruning for Large Language Models via Policy Gradient15 Jun 2024
- 2024The Max-Min Formulation of Multi-Objective Reinforcement Learning: From Theory to a Model-Free Algorithm12 Jun 2024
- 2024Full-Atom Peptide Design based on Multi-modal Flow Matching2 Jun 2024
- 2024Exact Solution to Data-Driven Inverse Optimization of MILPs in Finite Time via Gradient-Based Methods23 May 2024
- 2024Primal Methods for Variational Inequality Problems with Functional Constraints19 Mar 2024
- 2024Dirichlet Flow Matching with Applications to DNA Sequence Design8 Feb 2024
- 2023TERM Model: Tensor Ring Mixture Model for Density Estimation13 Dec 2023
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- 2023MKL-L0/1-SVM23 Aug 2023
- 2023An Online Multiple Kernel Parallelizable Learning Scheme19 Aug 2023
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- 2023Policy Gradient Algorithms for Robust MDPs with Non-Rectangular Uncertainty Sets30 May 2023
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- 2023Generating Adversarial Examples with Task Oriented Multi-Objective Optimization26 Apr 2023
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- 2023Scalable Randomized Kernel Methods for Multiview Data Integration and Prediction10 Apr 2023
- 2023Inaccurate Label Distribution Learning25 Feb 2023
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- 2023On the Robustness of Randomized Ensembles to Adversarial Perturbations2 Feb 2023
- 2023A Novel Framework for Policy Mirror Descent with General Parameterization and Linear Convergence30 Jan 2023
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50 newest of 65 All 65 (JSON)
- 2024Dirichlet Flow Matching with Applications to DNA Sequence Designcited by 113
- 2021Antipodes of Label Differential Privacy: PATE and ALIBIcited by 52
- 2024Full-Atom Peptide Design based on Multi-modal Flow Matchingcited by 34
- 2023Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithmscited by 33
- 2021Gradient play in stochastic games: stationary points, convergence, and sample complexitycited by 32
- 2023A Novel Framework for Policy Mirror Descent with General Parameterization and Linear Convergencecited by 30
- 2023Policy Gradient Algorithms for Robust MDPs with Non-Rectangular Uncertainty Setscited by 15
- 2021Fast and High-Quality Blind Multi-Spectral Image Pansharpeningcited by 13
- 2021The Hitchhiker's Guide to Prior-Shift Adaptationcited by 13
- 2022Robust Group Synchronization via Quadratic Programmingcited by 10
- 2023Inaccurate Label Distribution Learningcited by 10
- 2025Foundations of Top-k Decoding For Language Modelscited by 10
- 2024Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extensioncited by 9
12 most cited of 58 All 58 (JSON)
- 2026Leaner Transformers Can Easily Learn to Cluster7 Oct 2026
- 2026Accelerated Algorithm for Sparse Regularized Partial Optimal Transport30 Sep 2026
- 2026Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize24 Aug 2026
- 2026Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programs24 Jul 2026
- 2026COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering20 Jul 2026
- 2026Polyhedral Unmixing: Bridging Semantic Segmentation with Hyperspectral Unmixing via Polyhedral-Cone Partitioning31 Mar 2026
- 2026Compensating Visual Insufficiency with Stratified Language Guidance for Long-Tail Class Incremental Learning23 Mar 2026
- 2026SoftJAX & SoftTorch: Empowering Automatic Differentiation Libraries with Informative Gradients9 Mar 2026
- 2026ABM-UDE: Developing Surrogates for Epidemic Agent-Based Models via Scientific Machine Learning25 Feb 2026
- 2025Maximum Risk Minimization with Random Forests11 Dec 2025
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- 2025Geometry Denoising with Preferred Normal Vectors6 Nov 2025
12 newest of 58 All 58 (JSON)