Duality in Multi-View Restricted Kernel Machines

TL;DR

This paper introduces a unified primal-dual multi-view framework for restricted kernel machines that encompasses existing methods, providing theoretical insights and experimental validation on time series data.

Contribution

It unifies various restricted kernel machine methods into a single framework, deriving primal and dual representations and demonstrating their equivalence.

Findings

Primal and dual formulations can be made fully equivalent through rescaling.

The framework applies to both supervised and unsupervised settings.

Experimental results validate the theoretical equivalence and reveal relationships between methods.

Abstract

We propose a unifying setting that combines existing restricted kernel machine methods into a single primal-dual multi-view framework for kernel principal component analysis in both supervised and unsupervised settings. We derive the primal and dual representations of the framework and relate different training and inference algorithms from a theoretical perspective. We show how to achieve full equivalence in primal and dual formulations by rescaling primal variables. Finally, we experimentally validate the equivalence and provide insight into the relationships between different methods on a number of time series data sets by recursively forecasting unseen test data and visualizing the learned features.