# Distance-Ratio-Based Formulation for Metric Learning

arXiv: https://arxiv.org/abs/2201.08676 · HTML: https://mlsanity.com/paper/2201.08676/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 21 Jan 2022.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [Additive Margin Softmax for Face Verification](https://mlsanity.com/paper/1801.05599/) (2018)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Infinite Mixture Prototypes for Few-Shot Learning](https://mlsanity.com/paper/1902.04552/) (2019)
- [On Controllable Sparse Alternatives to Softmax](https://mlsanity.com/paper/1810.11975/) (2018)

## Built on by (most cited first, 1 of 1)

- [Inspecting class hierarchies in classification-based metric learning models](https://mlsanity.com/paper/2301.11065/) (2023)

## Abstract (arXiv)

In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric learning. Like softmax-based formulation for metric learning, it models p(y=c|x'), which is a probability that a query point x' belongs to a class c. The DR formulation has two useful properties. First, the corresponding loss is not affected by scale changes of an embedding. Second, it outputs the optimal (maximum or minimum) classification confidence scores on representing points for classes. To demonstrate the effectiveness of our formulation, we conduct few-shot classification experiments using softmax-based and DR formulations on CUB and mini-ImageNet datasets. The results show that DR formulation generally enables faster and more stable metric learning than the softmax-based formulation. As a result, using DR formulation achieves improved or comparable generalization performances.