[Paper Review] Large-scale Distance Metric Learning with Uncertainty

Qi Qian, Jiasheng Tang+3 more|arXiv (Cornell University)|May 25, 2018

Domain Adaptation and Few-Shot Learning19 references3 citations

TL;DR

This paper proposes Margin Preserving Metric Learning (MaPML), a large-scale distance metric learning framework that jointly learns a robust distance metric and clean latent examples from noisy, uncertain data. By training on a small set of latent examples instead of raw data, MaPML accelerates convergence, improves robustness to distortions, and preserves large margins for original data—achieving state-of-the-art accuracy on CIFAR-10, CIFAR-100, and ImageNet with significantly faster training than prior methods.

ABSTRACT

Distance metric learning (DML) has been studied extensively in the past decades for its superior performance with distance-based algorithms. Most of the existing methods propose to learn a distance metric with pairwise or triplet constraints. However, the number of constraints is quadratic or even cubic in the number of the original examples, which makes it challenging for DML to handle the large-scale data set. Besides, the real-world data may contain various uncertainty, especially for the image data. The uncertainty can mislead the learning procedure and cause the performance degradation. By investigating the image data, we find that the original data can be observed from a small set of clean latent examples with different distortions. In this work, we propose the margin preserving metric learning framework to learn the distance metric and latent examples simultaneously. By leveraging the ideal properties of latent examples, the training efficiency can be improved significantly while the learned metric also becomes robust to the uncertainty in the original data. Furthermore, we can show that the metric is learned from latent examples only, but it can preserve the large margin property even for the original data. The empirical study on the benchmark image data sets demonstrates the efficacy and efficiency of the proposed method.

Motivation & Objective

• To address the computational infeasibility of large-scale distance metric learning (DML) due to the quadratic or cubic growth of triplet constraints.
• To improve robustness to data uncertainty—especially in image data with distortions like pose, illumination, and noise—by modeling data as perturbations of clean latent examples.
• To enable efficient active-set optimization in DML by reducing the number of training examples to a small set of latent examples.
• To ensure that the learned metric preserves large margins not only on latent examples but also on the original, noisy data.
• To demonstrate the efficacy and efficiency of the proposed method on large-scale benchmarks, including ImageNet.

Proposed method

• The method introduces a margin-preserving metric learning framework that jointly optimizes the distance metric and latent examples from the same training data.
• It models each original data point as a perturbed version of a clean latent example, reducing data uncertainty and improving generalization.
• The framework uses active triplet constraints, where only violated triplets are processed, and leverages the small size of latent examples to make this step computationally feasible.
• The optimization is performed via a subproblem-solving approach with a cutting-plane method, enabling fast convergence.
• The learned metric is applied to the original data, and the large margin property is theoretically and empirically shown to be preserved.
• The method directly uses pixel-level features without requiring pre-trained networks, allowing recovery of interpretable latent examples as images.

Experimental results

Research questions

• RQ1 Can learning from a small set of clean latent examples significantly reduce the computational cost of large-scale distance metric learning?
• RQ2 Does learning from latent examples improve robustness to data uncertainty such as image distortions?
• RQ3 Can a metric learned solely on latent examples preserve large margins for the original, noisy data?
• RQ4 How does the proposed method compare in accuracy and efficiency to existing DML methods on large-scale benchmarks like ImageNet?
• RQ5 Can the active-set strategy be efficiently applied in large-scale DML when training on latent examples instead of raw data?

Key findings

• On CIFAR-10, MaPML achieved a test error rate of 12.64% ± 0.16, outperforming LMNN (13.62% ± 0.12) and OASIS (15.22% ± 0.18).
• On CIFAR-100, MaPML achieved 34.70% ± 0.16 error rate, significantly better than OASIS (42.46% ± 0.21) and HR-SGD (42.53% ± 0.19).
• On ImageNet, MaPML reduced the test error to 33.92% ± 0.09, a 1.7% improvement over the baseline Euclidean metric (35.65%), despite using features from a pre-trained ResNet18.
• MaPML trained on ImageNet in about one hour, while LMNN did not complete training within 24 hours, demonstrating superior scalability.
• The inference time was reduced from 0.15s per image using original data to 0.007s using latent examples, enabling real-time deployment.
• Visualizations confirmed that original images are well-explained as distortions of learned latent examples, validating the model's data generation assumption.