# Metric Learning with Adaptive Density Discrimination

arXiv: https://arxiv.org/abs/1511.05939 · HTML: https://mlsanity.com/paper/1511.05939/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2015.

## Built on by (most cited first, 30 of 40)

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- [Offline-Online Associated Camera-Aware Proxies for Unsupervised Person Re-identification](https://mlsanity.com/paper/2201.05820/) (2022)
- [Towards Improved Proxy-based Deep Metric Learning via Data-Augmented Domain Adaptation](https://mlsanity.com/paper/2401.00617/) (2024)
- [Distance-Forward Learning: Enhancing the Forward-Forward Algorithm Towards High-Performance On-Chip Learning](https://mlsanity.com/paper/2408.14925/) (2024)
- [Anomaly Detection with Score Distribution Discrimination](https://mlsanity.com/paper/2306.14403/) (2023)
- [Improving Deep Metric Learning by Divide and Conquer](https://mlsanity.com/paper/2109.04003/) (2021)
- [Vec2Face-v2: Unveil Human Faces from their Blackbox Features via Attention-based Network in Face Recognition](https://mlsanity.com/paper/2209.04920/) (2022)
- [Deep Metric Learning with Chance Constraints](https://mlsanity.com/paper/2209.09060/) (2022)
- [ProS: Facial Omni-Representation Learning via Prototype-based Self-Distillation](https://mlsanity.com/paper/2311.01929/) (2023)
- [Beyond Accuracy: Statistical Measures and Benchmark for Evaluation of Representation from Self-Supervised Learning](https://mlsanity.com/paper/2312.01118/) (2023)
- [A Framework to Enhance Generalization of Deep Metric Learning methods using General Discriminative Feature Learning and Class Adversarial Neural Networks](https://mlsanity.com/paper/2106.06420/) (2021)
- [Ensemble of Loss Functions to Improve Generalizability of Deep Metric Learning methods](https://mlsanity.com/paper/2107.01130/) (2021)
- [AUTOSHAPE: An Autoencoder-Shapelet Approach for Time Series Clustering](https://mlsanity.com/paper/2208.04313/) (2022)
- [Improving safety in physical human-robot collaboration via deep metric learning](https://mlsanity.com/paper/2302.11933/) (2023)
- [Controlling Class Layout for Deep Ordinal Classification via Constrained Proxies Learning](https://mlsanity.com/paper/2303.00396/) (2023)
- [Focal Inferential Infusion Coupled with Tractable Density Discrimination for Implicit Hate Detection](https://mlsanity.com/paper/2309.11896/) (2023)
- [Enhancing Interpretability Through Loss-Defined Classification Objective in Structured Latent Spaces](https://mlsanity.com/paper/2412.08515/) (2024)
- [GCCN: Global Context Convolutional Network](https://mlsanity.com/paper/2110.11664/) (2021)
- [VISHIEN-MAAT: Scrollytelling visualization design for explaining Siamese Neural Network concept to non-technical users](https://mlsanity.com/paper/2304.03288/) (2023)
- [Learning for Transductive Threshold Calibration in Open-World Recognition](https://mlsanity.com/paper/2305.12039/) (2023)
- [Fantastic DNN Classifiers and How to Identify them without Data](https://mlsanity.com/paper/2305.15563/) (2023)
- [CoNe: Contrast Your Neighbours for Supervised Image Classification](https://mlsanity.com/paper/2308.10761/) (2023)
- [Hyperspectral Image Analysis in Single-Modal and Multimodal setting using Deep Learning Techniques](https://mlsanity.com/paper/2403.01546/) (2024)
- [Robust Multimodal Learning for Ophthalmic Disease Grading via Disentangled Representation](https://mlsanity.com/paper/2503.05319/) (2025)
- [Adaptive Riemannian Graph Neural Networks](https://mlsanity.com/paper/2508.02600/) (2025)
- [SVMax: A Feature Embedding Regularizer](https://mlsanity.com/paper/2103.02770/) (2021)
- [Class-Agnostic Segmentation Loss and Its Application to Salient Object Detection and Segmentation](https://mlsanity.com/paper/2108.04226/) (2021)

## Abstract (arXiv)

Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40%. In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25% relative gains on the softmax classifier and 25-50% on triplet loss in these tasks.