在再生核希尔伯特空间中建立度量学习的理论框架，填补了非线性方法的理论空白。
Metric Learning in an RKHS
- 提出基于再生核希尔伯特空间的度量学习通用框架
- 给出新泛化界和样本复杂度分析，理论严谨
- 适用于图像检索、推荐系统等场景，适合理论研究者
从三元组比较（如“你觉得项目h更像项目i还是项目j？”）中学习度量，在图像检索、推荐系统和认知心理学等领域具有关键作用。目标是学习一个反映这些比较的再生核希尔伯特空间（RKHS）中的度量。尽管核方法和神经网络在非线性度量学习中表现出良好实证性能，但其理论基础仍不充分。此前工作仅对欧氏空间（即标准 ℝ^d）这一特例有完整理论。本文构建了通用的RKHS度量学习框架，提供新的泛化保证与样本复杂度边界，并通过模拟及真实数据集实验验证。代码已公开于 https://github.com/RamyaLab/metric-learning-RKHS。
原文摘要 · Abstract (English)
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 $\mathbb{R}^d$; there is a comprehensive theory for metric learning in $\mathbb{R}^d$. 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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