# Piecewise-Linear Manifolds for Deep Metric Learning

arXiv: https://arxiv.org/abs/2403.14977 · HTML: https://mlsanity.com/paper/2403.14977/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 43 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [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)
- [Discriminative Unsupervised Feature Learning with Exemplar Convolutional Neural Networks](https://mlsanity.com/paper/1406.6909/) (2014)
- [Unsupervised Embedding Learning via Invariant and Spreading Instance Feature](https://mlsanity.com/paper/1904.03436/) (2019)
- [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)
- [SoftTriple Loss: Deep Metric Learning Without Triplet Sampling](https://mlsanity.com/paper/1909.05235/) (2019)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [ProxyNCA++: Revisiting and Revitalizing Proxy Neighborhood Component Analysis](https://mlsanity.com/paper/2004.01113/) (2020)
- [Unsupervised Deep Learning by Neighbourhood Discovery](https://mlsanity.com/paper/1904.11567/) (2019)
- [Mining on Manifolds: Metric Learning without Labels](https://mlsanity.com/paper/1803.11095/) (2018)
- [Unsupervised Deep Metric Learning with Transformed Attention Consistency and Contrastive Clustering Loss](https://mlsanity.com/paper/2008.04378/) (2020)
- [Self-Taught Metric Learning without Labels](https://mlsanity.com/paper/2205.01903/) (2022)
- [The Importance of Metric Learning for Robotic Vision: Open Set Recognition and Active Learning](https://mlsanity.com/paper/1902.10363/) (2019)
- [Unsupervised Deep Metric Learning via Orthogonality based Probabilistic Loss](https://mlsanity.com/paper/2008.09880/) (2020)
- [Unsupervised Deep Metric Learning via Auxiliary Rotation Loss](https://mlsanity.com/paper/1911.07072/) (2019)

## Built on by (most cited first, 4 of 4)

- [Improving Multi-label Recognition using Class Co-Occurrence Probabilities](https://mlsanity.com/paper/2404.16193/) (2024)
- [Potential Field Based Deep Metric Learning](https://mlsanity.com/paper/2405.18560/) (2024)
- [Rethinking Prompting Strategies for Multi-Label Recognition with Partial Annotations](https://mlsanity.com/paper/2409.08381/) (2024)
- [Protocode: Prototype-Driven Interpretability for Code Generation in LLMs](https://mlsanity.com/paper/2509.25247/) (2025)

## Abstract (arXiv)

Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a deep network. For this purpose, we propose to model the high-dimensional data manifold using a piecewise-linear approximation, with each low-dimensional linear piece approximating the data manifold in a small neighborhood of a point. These neighborhoods are used to estimate similarity between data points. We empirically show that this similarity estimate correlates better with the ground truth than the similarity estimates of current state-of-the-art techniques. We also show that proxies, commonly used in supervised metric learning, can be used to model the piecewise-linear manifold in an unsupervised setting, helping improve performance. Our method outperforms existing unsupervised metric learning approaches on standard zero-shot image retrieval benchmarks.