# Elliptical Ordinal Embedding

arXiv: https://arxiv.org/abs/2105.10457 · HTML: https://mlsanity.com/paper/2105.10457/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 26 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 8 of 8)

- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions](https://mlsanity.com/paper/1805.07594/) (2018)
- [Cost-Effective HITs for Relative Similarity Comparisons](https://mlsanity.com/paper/1404.3291/) (2014)
- [Finite Sample Prediction and Recovery Bounds for Ordinal Embedding](https://mlsanity.com/paper/1606.07081/) (2016)
- [Crowdsourced correlation clustering with relative distance comparisons](https://mlsanity.com/paper/1709.08459/) (2017)
- [Comparison Based Learning from Weak Oracles](https://mlsanity.com/paper/1802.06942/) (2018)

## Abstract (arXiv)

Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item j is closer to item i than item k". Typically, each object is mapped onto a point vector in a low dimensional metric space. We argue that mapping to a density instead of a point vector provides some interesting advantages, including an inherent reflection of the uncertainty about the representation itself and its relative location in the space. Indeed, in this paper, we propose to embed each object as a Gaussian distribution. We investigate the ability of these embeddings to capture the underlying structure of the data while satisfying the constraints, and explore properties of the representation. Experiments on synthetic and real-world datasets showcase the advantages of our approach. In addition, we illustrate the merit of modelling uncertainty, which enriches the visual perception of the mapped objects in the space.