# Metric Learning in an RKHS

arXiv: https://arxiv.org/abs/2508.04476 · HTML: https://mlsanity.com/paper/2508.04476/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 67 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 21 of 21)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [PAL: Pluralistic Alignment Framework for Learning from Heterogeneous Preferences](https://mlsanity.com/paper/2406.08469/) (2024)
- [Clustering with Noisy Queries](https://mlsanity.com/paper/1706.07510/) (2017)
- [Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations](https://mlsanity.com/paper/2207.06503/) (2022)
- [Crowdsourcing via Pairwise Co-occurrences: Identifiability and Algorithms](https://mlsanity.com/paper/1909.12325/) (2019)
- [Cost-Effective HITs for Relative Similarity Comparisons](https://mlsanity.com/paper/1404.3291/) (2014)
- [Simultaneous Preference and Metric Learning from Paired Comparisons](https://mlsanity.com/paper/2009.02302/) (2020)
- [Learning Low-Dimensional Metrics](https://mlsanity.com/paper/1709.06171/) (2017)
- [Sample complexity of learning Mahalanobis distance metrics](https://mlsanity.com/paper/1505.02729/) (2015)
- [One for All: Simultaneous Metric and Preference Learning over Multiple Users](https://mlsanity.com/paper/2207.03609/) (2022)
- [Semisupervised Clustering by Queries and Locally Encodable Source Coding](https://mlsanity.com/paper/1904.00507/) (2019)
- [Transfer Learning with Kernel Methods](https://mlsanity.com/paper/2211.00227/) (2022)
- [Generalization analysis with deep ReLU networks for metric and similarity learning](https://mlsanity.com/paper/2405.06415/) (2024)
- [Mixed Membership Graph Clustering via Systematic Edge Query](https://mlsanity.com/paper/2011.12988/) (2020)
- [Perceptual adjustment queries and an inverted measurement paradigm for low-rank metric learning](https://mlsanity.com/paper/2309.04626/) (2023)
- [Metric Learning from Limited Pairwise Preference Comparisons](https://mlsanity.com/paper/2403.19629/) (2024)
- [Active metric learning and classification using similarity queries](https://mlsanity.com/paper/2202.01953/) (2022)

## Abstract (arXiv)

Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image retrieval, recommendation systems, and cognitive psychology. The goal is to learn a metric in the RKHS that reflects the comparisons. Nonlinear metric learning using kernel methods and neural networks have shown great empirical promise. While previous works have addressed certain aspects of this problem, there is little or no theoretical understanding of such methods. The exception is the special (linear) case in which the RKHS is the standard Euclidean space ℝd; there is a comprehensive theory for metric learning in ℝd. This paper develops a general RKHS framework for metric learning and provides novel generalization guarantees and sample complexity bounds. We validate our findings through a set of simulations and experiments on real datasets. Our code is publicly available at https://github.com/RamyaLab/metric-learning-RKHS.