# Metric Learning With HORDE: High-Order Regularizer for Deep Embeddings

## TL;DR

This paper introduces HORDE, a high-order regularizer for deep metric learning that improves the robustness and discriminability of image representations by enforcing distributional consistency among similar images.

## Contribution

The paper proposes a novel distribution-aware regularizer called HORDE, which enhances deep feature representations for metric learning by reducing scattering and improving robustness.

## Key findings

- Achieved state-of-the-art results on four benchmark datasets.
- Demonstrated improved robustness to outliers and occlusions.
- Provided theoretical analysis supporting the regularizer's effectiveness.

## Abstract

Learning an effective similarity measure between image representations is key to the success of recent advances in visual search tasks (e.g. verification or zero-shot learning). Although the metric learning part is well addressed, this metric is usually computed over the average of the extracted deep features. This representation is then trained to be discriminative. However, these deep features tend to be scattered across the feature space. Consequently, the representations are not robust to outliers, object occlusions, background variations, etc. In this paper, we tackle this scattering problem with a distribution-aware regularization named HORDE. This regularizer enforces visually-close images to have deep features with the same distribution which are well localized in the feature space. We provide a theoretical analysis supporting this regularization effect. We also show the effectiveness of our approach by obtaining state-of-the-art results on 4 well-known datasets (Cub-200-2011, Cars-196, Stanford Online Products and Inshop Clothes Retrieval).