mlsanityData to 7 Oct 2026

Metric Learning in an RKHS

arXiv 2508.04476 ↗First posted 6 Aug 2025stat.ML cs.AI cs.LGcited by 0

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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.

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References · 21

  1. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 633
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  11. 2020Simultaneous Preference and Metric Learning from Paired Comparisonscited by 10
  12. 2017Learning Low-Dimensional Metricscited by 9
9 more
  1. 2015Sample complexity of learning Mahalanobis distance metricscited by 7
  2. 2022One for All: Simultaneous Metric and Preference Learning over Multiple Userscited by 6
  3. 2019Semisupervised Clustering by Queries and Locally Encodable Source Codingcited by 5
  4. 2022Transfer Learning with Kernel Methodscited by 5
  5. 2020Mixed Membership Graph Clustering via Systematic Edge Querycited by 3
  6. 2023Perceptual adjustment queries and an inverted measurement paradigm for low-rank metric learningcited by 3
  7. 2024Metric Learning from Limited Pairwise Preference Comparisonscited by 3
  8. 2024Generalization analysis with deep ReLU networks for metric and similarity learningcited by 3
  9. 2022Active metric learning and classification using similarity queriescited by 2

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