# Clustering Unclustered Data: Unsupervised Binary Labeling of Two Datasets Having Different Class Balances

arXiv: https://arxiv.org/abs/1305.0103 · HTML: https://mlsanity.com/paper/1305.0103/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2013.

## Built on by (most cited first, 4 of 4)

- [Class-Imbalanced Complementary-Label Learning via Weighted Loss](https://mlsanity.com/paper/2209.14189/) (2022)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervision](https://mlsanity.com/paper/2306.07036/) (2023)
- [Learning from Stochastic Labels](https://mlsanity.com/paper/2302.00299/) (2023)

## Abstract (arXiv)

We consider the unsupervised learning problem of assigning labels to unlabeled data. A naive approach is to use clustering methods, but this works well only when data is properly clustered and each cluster corresponds to an underlying class. In this paper, we first show that this unsupervised labeling problem in balanced binary cases can be solved if two unlabeled datasets having different class balances are available. More specifically, estimation of the sign of the difference between probability densities of two unlabeled datasets gives the solution. We then introduce a new method to directly estimate the sign of the density difference without density estimation. Finally, we demonstrate the usefulness of the proposed method against several clustering methods on various toy problems and real-world datasets.