Multi-view Metric Learning in Vector-valued Kernel Spaces

TL;DR

This paper introduces a novel multi-view metric learning method in vector-valued kernel spaces that captures multi-modal data structure, with scalable algorithms and theoretical justifications, outperforming existing methods on real datasets.

Contribution

It proposes a new convex optimization framework for joint metric and classifier learning in vector-valued kernels, including a scalable Nyström approximation for large datasets.

Findings

Effective multi-view metric learning demonstrated on real datasets.

Scalable Nyström approximation reduces computational complexity.

Theoretical analysis supports the method's validity.

Abstract

We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We formulate two convex optimization problems to jointly learn the metric and the classifier or regressor in kernel feature spaces. An iterative three-step multi-view metric learning algorithm is derived from the optimization problems. In order to scale the computation to large training sets, a block-wise Nystr{\"o}m approximation of the multi-view kernel matrix is introduced. We justify our approach theoretically and experimentally, and show its performance on real-world datasets against relevant state-of-the-art methods.