Piecewise-Linear Manifolds for Deep Metric Learning

TL;DR

This paper introduces a novel unsupervised deep metric learning method that models data manifolds with piecewise-linear approximations, leading to improved similarity estimation and better zero-shot image retrieval performance.

Contribution

It proposes a new approach to model high-dimensional data manifolds using piecewise-linear approximations in an unsupervised setting, enhancing similarity estimation.

Findings

Better correlation with ground truth similarity than existing methods

Proxies improve manifold modeling and performance

Outperforms state-of-the-art unsupervised metric learning methods

Abstract

Unsupervised deep metric learning (UDML) focuses on learning a semantic representation space using only unlabeled data. This challenging problem requires accurately estimating the similarity between data points, which is used to supervise a deep network. For this purpose, we propose to model the high-dimensional data manifold using a piecewise-linear approximation, with each low-dimensional linear piece approximating the data manifold in a small neighborhood of a point. These neighborhoods are used to estimate similarity between data points. We empirically show that this similarity estimate correlates better with the ground truth than the similarity estimates of current state-of-the-art techniques. We also show that proxies, commonly used in supervised metric learning, can be used to model the piecewise-linear manifold in an unsupervised setting, helping improve performance. Our method outperforms existing unsupervised metric learning approaches on standard zero-shot image retrieval benchmarks.