# Insights into Ordinal Embedding Algorithms: A Systematic Evaluation

arXiv: https://arxiv.org/abs/1912.01666 · HTML: https://mlsanity.com/paper/1912.01666/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2019.

## Built on by (most cited first, 10 of 10)

- [The Complexity of Finding Local Optima in Contrastive Learning](https://mlsanity.com/paper/2509.16898/) (2025)
- [Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch](https://mlsanity.com/paper/2605.03346/) (2026)
- [Scalable and Interpretable Representation Alignment with Ordinal Similarity](https://mlsanity.com/paper/2606.16379/) (2026)
- [Fast Interactive Search with a Scale-Free Comparison Oracle](https://mlsanity.com/paper/2306.01814/) (2023)
- [Measuring IIA Violations in Similarity Choices with Bayesian Models](https://mlsanity.com/paper/2508.14615/) (2025)
- [Cluster and then Embed: A Modular Approach for Visualization](https://mlsanity.com/paper/2509.03373/) (2025)
- [Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2512.03899/) (2025)
- [LORE: Jointly Learning the Intrinsic Dimensionality and Relative Similarity Structure From Ordinal Data](https://mlsanity.com/paper/2602.04192/) (2026)
- [Eliciting associations between clinical variables from LLMs via comparison questions across populations](https://mlsanity.com/paper/2605.06335/) (2026)
- [Optimal VC Dimension of Contrastive Learning with Margin](https://mlsanity.com/paper/2609.38834/) (2026)

## Abstract (arXiv)

The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item i closer to the item j or item k?". In recent years, numerous algorithms have been proposed to solve this problem. However, there does not exist a fair and thorough assessment of these embedding methods and therefore several key questions remain unanswered: Which algorithms perform better when the embedding dimension is constrained or few triplet comparisons are available? Which ones scale better with increasing sample size or dimension? In our paper, we address these questions and provide the first comprehensive and systematic empirical evaluation of existing algorithms as well as a new neural network approach. We find that simple, relatively unknown, non-convex methods consistently outperform all other algorithms, including elaborate approaches based on neural networks or landmark approaches. This finding can be explained by our insight that many of the non-convex optimization approaches do not suffer from local optima. Our comprehensive assessment is enabled by our unified library of popular embedding algorithms that leverages GPU resources and allows for fast and accurate embeddings of millions of data points.