Metric Learning in an RKHS
This work addresses the lack of theoretical understanding for nonlinear metric learning methods, which is important for applications like image retrieval and recommendation systems, though it is incremental by extending linear theory to a general RKHS framework.
The paper tackles the problem of metric learning from triplet comparisons in a Reproducing Kernel Hilbert Space (RKHS), providing novel generalization guarantees and sample complexity bounds, validated through simulations and experiments on real datasets.
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.