# Divide and Conquer the Embedding Space for Metric Learning

arXiv: https://arxiv.org/abs/1906.05990 · HTML: https://mlsanity.com/paper/1906.05990/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2019.

## Built on by (most cited first, 30 of 39)

- [Instance-level Image Retrieval using Reranking Transformers](https://mlsanity.com/paper/2103.12236/) (2021)
- [Learning Intra-Batch Connections for Deep Metric Learning](https://mlsanity.com/paper/2102.07753/) (2021)
- [Non-isotropy Regularization for Proxy-based Deep Metric Learning](https://mlsanity.com/paper/2203.08547/) (2022)
- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift](https://mlsanity.com/paper/2410.09836/) (2024)
- [It Takes Two to Tango: Mixup for Deep Metric Learning](https://mlsanity.com/paper/2106.04990/) (2021)
- [Deep Relational Metric Learning](https://mlsanity.com/paper/2108.10026/) (2021)
- [Integrating Language Guidance into Vision-based Deep Metric Learning](https://mlsanity.com/paper/2203.08543/) (2022)
- [A Non-isotropic Probabilistic Take on Proxy-based Deep Metric Learning](https://mlsanity.com/paper/2207.03784/) (2022)
- [Hierarchical Proxy-based Loss for Deep Metric Learning](https://mlsanity.com/paper/2103.13538/) (2021)
- [Characterizing Generalization under Out-Of-Distribution Shifts in Deep Metric Learning](https://mlsanity.com/paper/2107.09562/) (2021)
- [Leveraging Large Language Models for Multimodal Search](https://mlsanity.com/paper/2404.15790/) (2024)
- [Neural Embedding: Learning the Embedding of the Manifold of Physics Data](https://mlsanity.com/paper/2208.05484/) (2022)
- [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)
- [Multi-level Distance Regularization for Deep Metric Learning](https://mlsanity.com/paper/2102.04223/) (2021)
- [The Group Loss++: A deeper look into group loss for deep metric learning](https://mlsanity.com/paper/2204.01509/) (2022)
- [Improving Deep Metric Learning by Divide and Conquer](https://mlsanity.com/paper/2109.04003/) (2021)
- [Rethinking the Optimization of Average Precision: Only Penalizing Negative Instances before Positive Ones is Enough](https://mlsanity.com/paper/2102.04640/) (2021)
- [Was that so hard? Estimating human classification difficulty](https://mlsanity.com/paper/2203.11824/) (2022)
- [Deep Metric Learning with Chance Constraints](https://mlsanity.com/paper/2209.09060/) (2022)
- [Metric Learning from Limited Pairwise Preference Comparisons](https://mlsanity.com/paper/2403.19629/) (2024)
- [Intra-class Adaptive Augmentation with Neighbor Correction for Deep Metric Learning](https://mlsanity.com/paper/2211.16264/) (2022)
- [ProcSim: Proxy-based Confidence for Robust Similarity Learning](https://mlsanity.com/paper/2311.00668/) (2023)
- [Semi Supervised Learning For Few-shot Audio Classification By Episodic Triplet Mining](https://mlsanity.com/paper/2102.08074/) (2021)
- [Partitioning Image Representation in Contrastive Learning](https://mlsanity.com/paper/2203.10454/) (2022)
- [Generalized Sum Pooling for Metric Learning](https://mlsanity.com/paper/2308.09228/) (2023)
- [Find your Needle: Small Object Image Retrieval via Multi-Object Attention Optimization](https://mlsanity.com/paper/2503.07038/) (2025)
- [SPOT-Face: Forensic Face Identification using Attention Guided Optimal Transport](https://mlsanity.com/paper/2601.09229/) (2026)
- [LIGAR: Lightweight General-purpose Action Recognition](https://mlsanity.com/paper/2108.13153/) (2021)

## Abstract (arXiv)

Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the embedding space for all available data points, which may have a very complex non-uniform distribution with different notions of similarity between objects, e.g. appearance, shape, color or semantic meaning. Approaches for learning a single distance metric often struggle to encode all different types of relationships and do not generalize well. In this work, we propose a novel easy-to-implement divide and conquer approach for deep metric learning, which significantly improves the state-of-the-art performance of metric learning. Our approach utilizes the embedding space more efficiently by jointly splitting the embedding space and data into K smaller sub-problems. It divides both, the data and the embedding space into K subsets and learns K separate distance metrics in the non-overlapping subspaces of the embedding space, defined by groups of neurons in the embedding layer of the neural network. The proposed approach increases the convergence speed and improves generalization since the complexity of each sub-problem is reduced compared to the original one. We show that our approach outperforms the state-of-the-art by a large margin in retrieval, clustering and re-identification tasks on CUB200-2011, CARS196, Stanford Online Products, In-shop Clothes and PKU VehicleID datasets.