# Duality in Multi-View Restricted Kernel Machines

arXiv: https://arxiv.org/abs/2305.17251 · HTML: https://mlsanity.com/paper/2305.17251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Disentangled Representation Learning and Generation with Manifold Optimization](https://mlsanity.com/paper/2006.07046/) (2020)
- [Unsupervised Energy-based Out-of-distribution Detection using Stiefel-Restricted Kernel Machine](https://mlsanity.com/paper/2102.08443/) (2021)
- [Unsupervised learning of disentangled representations in deep restricted kernel machines with orthogonality constraints](https://mlsanity.com/paper/2011.12659/) (2020)
- [Convex Formulation for Kernel PCA and its Use in Semi-Supervised Learning](https://mlsanity.com/paper/1610.06811/) (2016)
- [Deep Kernel Principal Component Analysis for Multi-level Feature Learning](https://mlsanity.com/paper/2302.11220/) (2023)
- [Latent Space Exploration Using Generative Kernel PCA](https://mlsanity.com/paper/2105.13949/) (2021)
- [Unsupervised Neighborhood Propagation Kernel Layers for Semi-supervised Node Classification](https://mlsanity.com/paper/2301.13764/) (2023)
- [Multi-view Kernel PCA for Time series Forecasting](https://mlsanity.com/paper/2301.09811/) (2023)

## Built on by (most cited first, 1 of 1)

- [Generative Kernel Spectral Clustering](https://mlsanity.com/paper/2502.02185/) (2025)

## Abstract (arXiv)

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.