# A Survey on Metric Learning for Feature Vectors and Structured Data

arXiv: https://arxiv.org/abs/1306.6709 · HTML: https://mlsanity.com/paper/1306.6709/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2013.

## Built on by (most cited first, 30 of 58)

- [Task-Embedded Control Networks for Few-Shot Imitation Learning](https://mlsanity.com/paper/1810.03237/) (2018)
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- [Joint Embedding Self-Supervised Learning in the Kernel Regime](https://mlsanity.com/paper/2209.14884/) (2022)
- [Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey](https://mlsanity.com/paper/2201.09267/) (2022)
- [Equiangular Basis Vectors](https://mlsanity.com/paper/2303.11637/) (2023)
- [Local Metric Learning for Off-Policy Evaluation in Contextual Bandits with Continuous Actions](https://mlsanity.com/paper/2210.13373/) (2022)
- [Unsupervised Ground Metric Learning using Wasserstein Singular Vectors](https://mlsanity.com/paper/2102.06278/) (2021)
- [Planning from Pixels in Environments with Combinatorially Hard Search Spaces](https://mlsanity.com/paper/2110.06149/) (2021)
- [Empirical Evaluation and Theoretical Analysis for Representation Learning: A Survey](https://mlsanity.com/paper/2204.08226/) (2022)
- [LeanVec: Searching vectors faster by making them fit](https://mlsanity.com/paper/2312.16335/) (2023)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [A Comprehensive Empirical Study of Vision-Language Pre-trained Model for Supervised Cross-Modal Retrieval](https://mlsanity.com/paper/2201.02772/) (2022)
- [Beyond Simple Meta-Learning: Multi-Purpose Models for Multi-Domain, Active and Continual Few-Shot Learning](https://mlsanity.com/paper/2201.05151/) (2022)
- [Leveraging Self-Supervised Learning for Scene Classification in Child Sexual Abuse Imagery](https://mlsanity.com/paper/2403.01183/) (2024)
- [A Lightweight Measure of Classification Difficulty from Application Dataset Characteristics](https://mlsanity.com/paper/2404.05981/) (2024)
- [Calibrated simplex-mapping classification](https://mlsanity.com/paper/2103.02926/) (2021)
- [Self-Supervised Metric Learning in Multi-View Data: A Downstream Task Perspective](https://mlsanity.com/paper/2106.07138/) (2021)
- [Instance-Based Neural Dependency Parsing](https://mlsanity.com/paper/2109.13497/) (2021)
- [On Medians of (Randomized) Pairwise Means](https://mlsanity.com/paper/2211.00603/) (2022)
- [Towards Self-Adaptive Metric Learning On the Fly](https://mlsanity.com/paper/2104.01495/) (2021)
- [Towards Sharper Utility Bounds for Differentially Private Pairwise Learning](https://mlsanity.com/paper/2105.03033/) (2021)
- [Generalized quantum similarity learning](https://mlsanity.com/paper/2201.02310/) (2022)
- [Guided Unsupervised Learning by Subaperture Decomposition for Ocean SAR Image Retrieval](https://mlsanity.com/paper/2209.15034/) (2022)
- [M-VAAL: Multimodal Variational Adversarial Active Learning for Downstream Medical Image Analysis Tasks](https://mlsanity.com/paper/2306.12376/) (2023)
- [Enigma: Application-Layer Privacy for Quantum Optimization on Untrusted Computers](https://mlsanity.com/paper/2311.13546/) (2023)
- [Differentially Private Stochastic Gradient Descent with Low-Noise](https://mlsanity.com/paper/2209.04188/) (2022)

## Abstract (arXiv)

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.