# Robust Metric Learning based on the Rescaled Hinge Loss

## TL;DR

This paper introduces a robust metric learning method utilizing the Rescaled Hinge loss, effectively handling noisy and outlier-laden training data to improve distance function learning.

## Contribution

It formulates a new metric learning approach based on the Rescaled Hinge loss and develops an efficient HQ-based algorithm for robust performance.

## Key findings

- Outperforms state-of-the-art methods on real datasets
- Handles label noise and outliers effectively
- Demonstrates robustness in synthetic experiments

## Abstract

Distance/Similarity learning is a fundamental problem in machine learning. For example, kNN classifier or clustering methods are based on a distance/similarity measure. Metric learning algorithms enhance the efficiency of these methods by learning an optimal distance function from data. Most metric learning methods need training information in the form of pair or triplet sets. Nowadays, this training information often is obtained from the Internet via crowdsourcing methods. Therefore, this information may contain label noise or outliers leading to the poor performance of the learned metric. It is even possible that the learned metric functions perform worse than the general metrics such as Euclidean distance. To address this challenge, this paper presents a new robust metric learning method based on the Rescaled Hinge loss. This loss function is a general case of the popular Hinge loss and initially introduced in (Xu et al. 2017) to develop a new robust SVM algorithm. In this paper, we formulate the metric learning problem using the Rescaled Hinge loss function and then develop an efficient algorithm based on HQ (Half-Quadratic) to solve the problem. Experimental results on a variety of both real and synthetic datasets confirm that our new robust algorithm considerably outperforms state-of-the-art metric learning methods in the presence of label noise and outliers.

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Source: https://tomesphere.com/paper/1904.11711