# Adaptive neighborhood Metric learning

arXiv: https://arxiv.org/abs/2201.08314 · HTML: https://mlsanity.com/paper/2201.08314/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 20 Jan 2022.

## Builds on (most cited first, 23 of 23)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [In Defense of the Triplet Loss for Person Re-Identification](https://mlsanity.com/paper/1703.07737/) (2017)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Circle Loss: A Unified Perspective of Pair Similarity Optimization](https://mlsanity.com/paper/2002.10857/) (2020)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [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)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [Deep Metric Learning with Hierarchical Triplet Loss](https://mlsanity.com/paper/1810.06951/) (2018)
- [Smart Mining for Deep Metric Learning](https://mlsanity.com/paper/1704.01285/) (2017)
- [Ranked List Loss for Deep Metric Learning](https://mlsanity.com/paper/1903.03238/) (2019)
- [Optimization for deep learning: theory and algorithms](https://mlsanity.com/paper/1912.08957/) (2019)
- [Attention-based Ensemble for Deep Metric Learning](https://mlsanity.com/paper/1804.00382/) (2018)
- [Hardness-Aware Deep Metric Learning](https://mlsanity.com/paper/1903.05503/) (2019)
- [Deep Metric Learning with BIER: Boosting Independent Embeddings Robustly](https://mlsanity.com/paper/1801.04815/) (2018)
- [Geometric Mean Metric Learning](https://mlsanity.com/paper/1607.05002/) (2016)
- [Sparse Compositional Metric Learning](https://mlsanity.com/paper/1404.4105/) (2014)
- [Learning Local Metrics and Influential Regions for Classification](https://mlsanity.com/paper/1802.03452/) (2018)
- [Fine-Grained Visual Categorization via Multi-stage Metric Learning](https://mlsanity.com/paper/1402.0453/) (2014)

## Built on by (most cited first, 3 of 3)

- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Categorical Knowledge Fused Recognition: Fusing Hierarchical Knowledge with Image Classification through Aligning and Deep Metric Learning](https://mlsanity.com/paper/2407.20600/) (2024)
- [Enhance Hyperbolic Representation Learning via Second-order Pooling](https://mlsanity.com/paper/2410.22026/) (2024)

## Abstract (arXiv)

In this paper, we reveal that metric learning would suffer from serious inseparable problem if without informative sample mining. Since the inseparable samples are often mixed with hard samples, current informative sample mining strategies used to deal with inseparable problem may bring up some side-effects, such as instability of objective function, etc. To alleviate this problem, we propose a novel distance metric learning algorithm, named adaptive neighborhood metric learning (ANML). In ANML, we design two thresholds to adaptively identify the inseparable similar and dissimilar samples in the training procedure, thus inseparable sample removing and metric parameter learning are implemented in the same procedure. Due to the non-continuity of the proposed ANML, we develop an ingenious function, named log-exp mean function to construct a continuous formulation to surrogate it, which can be efficiently solved by the gradient descent method. Similar to Triplet loss, ANML can be used to learn both the linear and deep embeddings. By analyzing the proposed method, we find it has some interesting properties. For example, when ANML is used to learn the linear embedding, current famous metric learning algorithms such as the large margin nearest neighbor (LMNN) and neighbourhood components analysis (NCA) are the special cases of the proposed ANML by setting the parameters different values. When it is used to learn deep features, the state-of-the-art deep metric learning algorithms such as Triplet loss, Lifted structure loss, and Multi-similarity loss become the special cases of ANML. Furthermore, the log-exp mean function proposed in our method gives a new perspective to review the deep metric learning methods such as Prox-NCA and N-pairs loss. At last, promising experimental results demonstrate the effectiveness of the proposed method.