Piecewise-Linear Manifolds for Deep Metric Learning

Shubhang Bhatnagar, Narendra Ahuja
Conference on Parsimony and Learning, PMLR 234:269-281, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v234-bhatnagar24a, title = {Piecewise-Linear Manifolds for Deep Metric Learning}, author = {Bhatnagar, Shubhang and Ahuja, Narendra}, booktitle = {Conference on Parsimony and Learning}, pages = {269--281}, year = {2024}, editor = {Chi, Yuejie and Dziugaite, Gintare Karolina and Qu, Qing and Wang, Atlas Wang and Zhu, Zhihui}, volume = {234}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jan}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v234/bhatnagar24a/bhatnagar24a.pdf}, url = {https://proceedings.mlr.press/v234/bhatnagar24a.html}, 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.} }
Endnote
%0 Conference Paper %T Piecewise-Linear Manifolds for Deep Metric Learning %A Shubhang Bhatnagar %A Narendra Ahuja %B Conference on Parsimony and Learning %C Proceedings of Machine Learning Research %D 2024 %E Yuejie Chi %E Gintare Karolina Dziugaite %E Qing Qu %E Atlas Wang Wang %E Zhihui Zhu %F pmlr-v234-bhatnagar24a %I PMLR %P 269--281 %U https://proceedings.mlr.press/v234/bhatnagar24a.html %V 234 %X 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.
APA
Bhatnagar, S. & Ahuja, N.. (2024). Piecewise-Linear Manifolds for Deep Metric Learning. Conference on Parsimony and Learning, in Proceedings of Machine Learning Research 234:269-281 Available from https://proceedings.mlr.press/v234/bhatnagar24a.html.

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