Piecewise-Linear Manifolds for Deep Metric Learning

• URL: http://arxiv.org/abs/2403.14977v1
• Date: Fri, 22 Mar 2024 06:22:20 GMT
• Title: Piecewise-Linear Manifolds for Deep Metric Learning
• Authors: Shubhang Bhatnagar, Narendra Ahuja,
• Abstract summary: Unsupervised deep metric learning focuses on learning a semantic representation space using only unlabeled data. 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. We empirically show that this similarity estimate correlates better with the ground truth than the similarity estimates of current state-of-the-art techniques.
• Score: 8.670873561640903
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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