# Safe Triplet Screening for Distance Metric Learning

arXiv: https://arxiv.org/abs/1802.03923 · HTML: https://mlsanity.com/paper/1802.03923/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

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

- [Expanding boundaries of Gap Safe screening](https://mlsanity.com/paper/2102.10846/) (2021)
- [Auxiliary Cross-Modal Representation Learning with Triplet Loss Functions for Online Handwriting Recognition](https://mlsanity.com/paper/2202.07901/) (2022)
- [Efficient Model Selection for Predictive Pattern Mining Model by Safe Pattern Pruning](https://mlsanity.com/paper/2306.13561/) (2023)
- [Safe Screening for Unbalanced Optimal Transport](https://mlsanity.com/paper/2307.00247/) (2023)

## Abstract (arXiv)

We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of possible triplets is quite huge even for a small dataset. Our safe triplet screening identifies triplets which can be safely removed from the optimization problem without losing the optimality. Compared with existing safe screening studies, triplet screening is particularly significant because of (1) the huge number of possible triplets, and (2) the semi-definite constraint in the optimization. We derive several variants of screening rules, and analyze their relationships. Numerical experiments on benchmark datasets demonstrate the effectiveness of safe triplet screening.