# Efficient Distance Metric Learning by Adaptive Sampling and Mini-Batch Stochastic Gradient Descent (SGD)

arXiv: https://arxiv.org/abs/1304.1192 · HTML: https://mlsanity.com/paper/1304.1192/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2013.

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

- [Subspace based Federated Unlearning](https://mlsanity.com/paper/2302.12448/) (2023)
- [Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case](https://mlsanity.com/paper/2307.11782/) (2023)
- [FedCME: Client Matching and Classifier Exchanging to Handle Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2307.08574/) (2023)
- [DAAL: Density-Aware Adaptive Line Margin Loss for Multi-Modal Deep Metric Learning](https://mlsanity.com/paper/2410.05438/) (2024)

## Abstract (arXiv)

Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to be a positive semi-definite (PSD) matrix. Although stochastic gradient descent (SGD) has been successfully applied to improve the efficiency of DML, it can still be computationally expensive because in order to ensure that the solution is a PSD matrix, it has to, at every iteration, project the updated distance metric onto the PSD cone, an expensive operation. We address this challenge by developing two strategies within SGD, i.e. mini-batch and adaptive sampling, to effectively reduce the number of updates (i.e., projections onto the PSD cone) in SGD. We also develop hybrid approaches that combine the strength of adaptive sampling with that of mini-batch online learning techniques to further improve the computational efficiency of SGD for DML. We prove the theoretical guarantees for both adaptive sampling and mini-batch based approaches for DML. We also conduct an extensive empirical study to verify the effectiveness of the proposed algorithms for DML.