# Denoising Multi-Similarity Formulation: A Self-paced Curriculum-Driven Approach for Robust Metric Learning

arXiv: https://arxiv.org/abs/2211.11751 · HTML: https://mlsanity.com/paper/2211.11751/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Jo-SRC: A Contrastive Approach for Combating Noisy Labels](https://mlsanity.com/paper/2103.13029/) (2021)
- [Learning by tracking: Siamese CNN for robust target association](https://mlsanity.com/paper/1604.07866/) (2016)
- [A Zero-Shot Framework for Sketch-based Image Retrieval](https://mlsanity.com/paper/1807.11724/) (2018)
- [Triplet-Center Loss for Multi-View 3D Object Retrieval](https://mlsanity.com/paper/1803.06189/) (2018)
- [Learning Descriptors for Object Recognition and 3D Pose Estimation](https://mlsanity.com/paper/1502.05908/) (2015)
- [NGC: A Unified Framework for Learning with Open-World Noisy Data](https://mlsanity.com/paper/2108.11035/) (2021)
- [Hard Sample Aware Noise Robust Learning for Histopathology Image Classification](https://mlsanity.com/paper/2112.03694/) (2021)
- [Zero-Shot Learning via Joint Latent Similarity Embedding](https://mlsanity.com/paper/1511.04512/) (2015)
- [Signal-to-Noise Ratio: A Robust Distance Metric for Deep Metric Learning](https://mlsanity.com/paper/1904.02616/) (2019)
- [3D Pose Estimation and 3D Model Retrieval for Objects in the Wild](https://mlsanity.com/paper/1803.11493/) (2018)
- [Improving Semantic Embedding Consistency by Metric Learning for Zero-Shot Classification](https://mlsanity.com/paper/1607.08085/) (2016)
- [Hard-Aware Point-to-Set Deep Metric for Person Re-identification](https://mlsanity.com/paper/1807.11206/) (2018)
- [Safe Sample Screening for Robust Support Vector Machine](https://mlsanity.com/paper/1912.11217/) (2019)
- [Robust Metric Learning based on the Rescaled Hinge Loss](https://mlsanity.com/paper/1904.11711/) (2019)

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

- [Globally Correlation-Aware Hard Negative Generation](https://mlsanity.com/paper/2411.13145/) (2024)
- [ROGPL: Robust Open-Set Graph Learning via Region-Based Prototype Learning](https://mlsanity.com/paper/2402.18495/) (2024)
- [Graph Multi-Similarity Learning for Molecular Property Prediction](https://mlsanity.com/paper/2401.17615/) (2024)

## Abstract (arXiv)

Deep Metric Learning (DML) is a group of techniques that aim to measure the similarity between objects through the neural network. Although the number of DML methods has rapidly increased in recent years, most previous studies cannot effectively handle noisy data, which commonly exists in practical applications and often leads to serious performance deterioration. To overcome this limitation, in this paper, we build a connection between noisy samples and hard samples in the framework of self-paced learning, and propose a underlineBalanced underlineSelf-underlinePaced underlineMetric underlineLearning (BSPML) algorithm with a denoising multi-similarity formulation, where noisy samples are treated as extremely hard samples and adaptively excluded from the model training by sample weighting. Especially, due to the pairwise relationship and a new balance regularization term, the sub-problem w.r.t. sample weights is a nonconvex quadratic function. To efficiently solve this nonconvex quadratic problem, we propose a doubly stochastic projection coordinate gradient algorithm. Importantly, we theoretically prove the convergence not only for the doubly stochastic projection coordinate gradient algorithm, but also for our BSPML algorithm. Experimental results on several standard data sets demonstrate that our BSPML algorithm has better generalization ability and robustness than the state-of-the-art robust DML approaches.