# Top-k Multiclass SVM

arXiv: https://arxiv.org/abs/1511.06683 · HTML: https://mlsanity.com/paper/1511.06683/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2015.

## Built on by (most cited first, 28 of 28)

- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Set-valued classification -- overview via a unified framework](https://mlsanity.com/paper/2102.12318/) (2021)
- [TkML-AP: Adversarial Attacks to Top-k Multi-Label Learning](https://mlsanity.com/paper/2108.00146/) (2021)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Fast, Differentiable and Sparse Top-k: a Convex Analysis Perspective](https://mlsanity.com/paper/2302.01425/) (2023)
- [Sum of Ranked Range Loss for Supervised Learning](https://mlsanity.com/paper/2106.03300/) (2021)
- [sigmoidF1: A Smooth F1 Score Surrogate Loss for Multilabel Classification](https://mlsanity.com/paper/2108.10566/) (2021)
- [Cardinality-Aware Set Prediction and Top-k Classification](https://mlsanity.com/paper/2407.07140/) (2024)
- [Differentiable Top-k Classification Learning](https://mlsanity.com/paper/2206.07290/) (2022)
- [Enhanced H-Consistency Bounds](https://mlsanity.com/paper/2407.13722/) (2024)
- [An Embedding Framework for the Design and Analysis of Consistent Polyhedral Surrogates](https://mlsanity.com/paper/2206.14707/) (2022)
- [Label Distributionally Robust Losses for Multi-class Classification: Consistency, Robustness and Adaptivity](https://mlsanity.com/paper/2112.14869/) (2021)
- [Stochastic smoothing of the top-K calibrated hinge loss for deep imbalanced classification](https://mlsanity.com/paper/2202.02193/) (2022)
- [Optimizing Partial Area Under the Top-k Curve: Theory and Practice](https://mlsanity.com/paper/2209.01398/) (2022)
- [Consistent Polyhedral Surrogates for Top-k Classification and Variants](https://mlsanity.com/paper/2207.08873/) (2022)
- [Why Ask One When You Can Ask k? Learning-to-Defer to the Top-k Experts](https://mlsanity.com/paper/2504.12988/) (2025)
- [Conformal Prediction for Long-Tailed Classification](https://mlsanity.com/paper/2507.06867/) (2025)
- [Multi-class Support Vector Machine with Maximizing Minimum Margin](https://mlsanity.com/paper/2312.06578/) (2023)
- [Fine-grained Generalization Analysis of Vector-valued Learning](https://mlsanity.com/paper/2104.14173/) (2021)
- [Top-k Classification and Cardinality-Aware Prediction](https://mlsanity.com/paper/2403.19625/) (2024)
- [Tensor Normalization and Full Distribution Training](https://mlsanity.com/paper/2109.02345/) (2021)
- [Welfare as a Guiding Principle for Machine Learning -- From Compass, to Lens, to Roadmap](https://mlsanity.com/paper/2502.11981/) (2025)
- [Provable Robust Saliency-based Explanations](https://mlsanity.com/paper/2212.14106/) (2022)
- [Top-K Pairwise Ranking: Bridging the Gap Among Ranking-Based Measures for Multi-Label Classification](https://mlsanity.com/paper/2407.06709/) (2024)
- [A two-head loss function for deep Average-K classification](https://mlsanity.com/paper/2303.18118/) (2023)
- [pSVM: Soft-margin SVMs with p-norm Hinge Loss](https://mlsanity.com/paper/2408.09908/) (2024)
- [Detecci'on Autom'atica de Patolog'ias en Notas Cl'inicas en Espa~nol Combinando Modelos de Lenguaje y Ontolog'ias M'edicos](https://mlsanity.com/paper/2410.00616/) (2024)
- [Automatic detection of diseases in Spanish clinical notes combining medical language models and ontologies](https://mlsanity.com/paper/2412.03176/) (2024)

## Abstract (arXiv)

Class ambiguity is typical in image classification problems with a large number of classes. When classes are difficult to discriminate, it makes sense to allow k guesses and evaluate classifiers based on the top-k error instead of the standard zero-one loss. We propose top-k multiclass SVM as a direct method to optimize for top-k performance. Our generalization of the well-known multiclass SVM is based on a tight convex upper bound of the top-k error. We propose a fast optimization scheme based on an efficient projection onto the top-k simplex, which is of its own interest. Experiments on five datasets show consistent improvements in top-k accuracy compared to various baselines.