# Bridging Ordinary-Label Learning and Complementary-Label Learning

arXiv: https://arxiv.org/abs/2002.02158 · HTML: https://mlsanity.com/paper/2002.02158/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2020.

## Built on by (most cited first, 11 of 11)

- [Learning from Similarity-Confidence Data](https://mlsanity.com/paper/2102.06879/) (2021)
- [Reduction from Complementary-Label Learning to Probability Estimates](https://mlsanity.com/paper/2209.09500/) (2022)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Multi-Class Classification from Single-Class Data with Confidences](https://mlsanity.com/paper/2106.08864/) (2021)
- [Intra-Cluster Mixup: An Effective Data Augmentation Technique for Complementary-Label Learning](https://mlsanity.com/paper/2509.17971/) (2025)
- [Invariance Learning based on Label Hierarchy](https://mlsanity.com/paper/2203.15549/) (2022)
- [ProPaLL: Probabilistic Partial Label Learning](https://mlsanity.com/paper/2208.09931/) (2022)
- [Complementary to Multiple Labels: A Correlation-Aware Correction Approach](https://mlsanity.com/paper/2302.12987/) (2023)
- [Appeal: Allow Mislabeled Samples the Chance to be Rectified in Partial Label Learning](https://mlsanity.com/paper/2312.11034/) (2023)
- [Q&A Label Learning](https://mlsanity.com/paper/2305.04539/) (2023)
- [Learning from Complementary Features](https://mlsanity.com/paper/2408.14788/) (2024)

## Abstract (arXiv)

A supervised learning framework has been proposed for the situation where each training data is provided with a complementary label that represents a class to which the pattern does not belong. In the existing literature, complementary-label learning has been studied independently from ordinary-label learning, which assumes that each training data is provided with a label representing the class to which the pattern belongs. However, providing a complementary label should be treated as equivalent to providing the rest of all the labels as the candidates of the one true class. In this paper, we focus on the fact that the loss functions for one-versus-all and pairwise classification corresponding to ordinary-label learning and complementary-label learning satisfy certain additivity and duality, and provide a framework which directly bridge those existing supervised learning frameworks. Further, we derive classification risk and error bound for any loss functions which satisfy additivity and duality.