# Classification from Pairwise Similarity and Unlabeled Data

arXiv: https://arxiv.org/abs/1802.04381 · HTML: https://mlsanity.com/paper/1802.04381/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

## Built on by (most cited first, 30 of 36)

- [Understanding Negative Samples in Instance Discriminative Self-supervised Representation Learning](https://mlsanity.com/paper/2102.06866/) (2021)
- [Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification](https://mlsanity.com/paper/2202.00395/) (2022)
- [On the Surrogate Gap between Contrastive and Supervised Losses](https://mlsanity.com/paper/2110.02501/) (2021)
- [Learning from Similarity-Confidence Data](https://mlsanity.com/paper/2102.06879/) (2021)
- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classification](https://mlsanity.com/paper/2102.00678/) (2021)
- [EEGMatch: Learning with Incomplete Labels for Semi-Supervised EEG-based Cross-Subject Emotion Recognition](https://mlsanity.com/paper/2304.06496/) (2023)
- [Learning with Proper Partial Labels](https://mlsanity.com/paper/2112.12303/) (2021)
- [Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimation](https://mlsanity.com/paper/2107.05045/) (2021)
- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Empirical Evaluation and Theoretical Analysis for Representation Learning: A Survey](https://mlsanity.com/paper/2204.08226/) (2022)
- [A Universal Unbiased Method for Classification from Aggregate Observations](https://mlsanity.com/paper/2306.11343/) (2023)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Contrastive Identification and Generation in the Limit](https://mlsanity.com/paper/2605.06211/) (2026)
- [Multi-Class Classification from Single-Class Data with Confidences](https://mlsanity.com/paper/2106.08864/) (2021)
- [Labels, Information, and Computation: Efficient Learning Using Sufficient Labels](https://mlsanity.com/paper/2104.09015/) (2021)
- [Learning from Label Proportions with Instance-wise Consistency](https://mlsanity.com/paper/2203.12836/) (2022)
- [A Generalized Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/2306.06894/) (2023)
- [Feature Normalization Prevents Collapse of Non-contrastive Learning Dynamics](https://mlsanity.com/paper/2309.16109/) (2023)
- [Learning from Positive and Unlabeled Data with Augmented Classes](https://mlsanity.com/paper/2207.13274/) (2022)
- [Robust Noisy Label Learning via Two-Stream Sample Distillation](https://mlsanity.com/paper/2404.10499/) (2024)
- [Unsupervised Pairwise Learning Optimization Framework for Cross-Corpus EEG-Based Emotion Recognition Based on Prototype Representation](https://mlsanity.com/paper/2508.11663/) (2025)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [RoLNiP: Robust Learning Using Noisy Pairwise Comparisons](https://mlsanity.com/paper/2303.02341/) (2023)
- [Q&A Label Learning](https://mlsanity.com/paper/2305.04539/) (2023)
- [Learning from Concealed Labels](https://mlsanity.com/paper/2412.02230/) (2024)
- [Learning from M-Tuple Dominant Positive and Unlabeled Data](https://mlsanity.com/paper/2506.15686/) (2025)
- [A Unified Empirical Risk Minimization Framework for Flexible N-Tuples Weak Supervision](https://mlsanity.com/paper/2507.07771/) (2025)
- [Learning from Similarity-Confidence and Confidence-Difference](https://mlsanity.com/paper/2508.05108/) (2025)
- [Learning from Uncertain Similarity and Unlabeled Data](https://mlsanity.com/paper/2509.11984/) (2025)

## Abstract (arXiv)

Supervised learning needs a huge amount of labeled data, which can be a big bottleneck under the situation where there is a privacy concern or labeling cost is high. To overcome this problem, we propose a new weakly-supervised learning setting where only similar (S) data pairs (two examples belong to the same class) and unlabeled (U) data points are needed instead of fully labeled data, which is called SU classification. We show that an unbiased estimator of the classification risk can be obtained only from SU data, and the estimation error of its empirical risk minimizer achieves the optimal parametric convergence rate. Finally, we demonstrate the effectiveness of the proposed method through experiments.