# Improving Deep Metric Learning by Divide and Conquer

arXiv: https://arxiv.org/abs/2109.04003 · HTML: https://mlsanity.com/paper/2109.04003/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 112 references that are in the map.
- First posted on arXiv 9 Sep 2021.

## Builds on (most cited first, 30 of 61)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [In Defense of the Triplet Loss for Person Re-Identification](https://mlsanity.com/paper/1703.07737/) (2017)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Meta-Transfer Learning for Few-Shot Learning](https://mlsanity.com/paper/1812.02391/) (2018)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [No Fuss Distance Metric Learning using Proxies](https://mlsanity.com/paper/1703.07464/) (2017)
- [Deep clustering: Discriminative embeddings for segmentation and separation](https://mlsanity.com/paper/1508.04306/) (2015)
- [Teacher-Student Curriculum Learning](https://mlsanity.com/paper/1707.00183/) (2017)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [Learning Fine-grained Image Similarity with Deep Ranking](https://mlsanity.com/paper/1404.4661/) (2014)
- [SoftTriple Loss: Deep Metric Learning Without Triplet Sampling](https://mlsanity.com/paper/1909.05235/) (2019)
- [Improving the Robustness of Deep Neural Networks via Stability Training](https://mlsanity.com/paper/1604.04326/) (2016)
- [Deep Metric Learning with Hierarchical Triplet Loss](https://mlsanity.com/paper/1810.06951/) (2018)
- [Learning to Compare Image Patches via Convolutional Neural Networks](https://mlsanity.com/paper/1504.03641/) (2015)
- [Deep Metric Learning with Angular Loss](https://mlsanity.com/paper/1708.01682/) (2017)

## Built on by (most cited first, 5 of 5)

- [Contrastive Bayesian Analysis for Deep Metric Learning](https://mlsanity.com/paper/2210.04402/) (2022)
- [Introspective Deep Metric Learning](https://mlsanity.com/paper/2309.09982/) (2023)
- [SCFlow: Implicitly Learning Style and Content Disentanglement with Flow Models](https://mlsanity.com/paper/2508.03402/) (2025)
- [Coded Residual Transform for Generalizable Deep Metric Learning](https://mlsanity.com/paper/2210.04180/) (2022)
- [A Dataset and Framework for Learning State-invariant Object Representations](https://mlsanity.com/paper/2404.06470/) (2024)

## Abstract (arXiv)

Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far from another. The target similarity on the training data is defined by user in form of ground-truth class labels. However, while the embedding space learns to mimic the user-provided similarity on the training data, it should also generalize to novel categories not seen during training. Besides user-provided groundtruth training labels, a lot of additional visual factors (such as viewpoint changes or shape peculiarities) exist and imply different notions of similarity between objects, affecting the generalization on the images unseen during training. However, existing approaches usually directly learn a single embedding space on all available training data, struggling to encode all different types of relationships, and do not generalize well. We propose to build a more expressive representation by jointly splitting the embedding space and the data hierarchically into smaller sub-parts. We successively focus on smaller subsets of the training data, reducing its variance and learning a different embedding subspace for each data subset. Moreover, the subspaces are learned jointly to cover not only the intricacies, but the breadth of the data as well. Only after that, we build the final embedding from the subspaces in the conquering stage. The proposed algorithm acts as a transparent wrapper that can be placed around arbitrary existing DML methods. Our approach significantly improves upon the state-of-the-art on image retrieval, clustering, and re-identification tasks evaluated using CUB200-2011, CARS196, Stanford Online Products, In-shop Clothes, and PKU VehicleID datasets.