# Robust Ordinal Embedding from Contaminated Relative Comparisons

arXiv: https://arxiv.org/abs/1812.01945 · HTML: https://mlsanity.com/paper/1812.01945/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2018.

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

- [Generalization Error Bound for Hyperbolic Ordinal Embedding](https://mlsanity.com/paper/2105.10475/) (2021)
- [Efficient Backdoor Defense in Multimodal Contrastive Learning: A Token-Level Unlearning Method for Mitigating Threats](https://mlsanity.com/paper/2409.19526/) (2024)
- [Active metric learning and classification using similarity queries](https://mlsanity.com/paper/2202.01953/) (2022)
- [UN-AVOIDS: Unsupervised and Nonparametric Approach for Visualizing Outliers and Invariant Detection Scoring](https://mlsanity.com/paper/2111.10010/) (2021)

## Abstract (arXiv)

Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner is well-known to suffer from sub-optimal solutions. In this paper, we propose a unified framework to jointly identify the contaminated comparisons and derive reliable embeddings. The merits of our method are three-fold: (1) By virtue of the proposed unified framework, the sub-optimality of traditional methods is largely alleviated; (2) The proposed method is aware of global inconsistency by minimizing a corresponding cost, while traditional methods only involve local inconsistency; (3) Instead of considering the nuclear norm heuristics, we adopt an exact solution for rank equality constraint. Our studies are supported by experiments with both simulated examples and real-world data. The proposed framework provides us a promising tool for robust ordinal embedding from the contaminated comparisons.