# Multi-view Kernel PCA for Time series Forecasting

arXiv: https://arxiv.org/abs/2301.09811 · HTML: https://mlsanity.com/paper/2301.09811/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 16 of 16)

- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Chickenpox Cases in Hungary: a Benchmark Dataset for Spatiotemporal Signal Processing with Graph Neural Networks](https://mlsanity.com/paper/2102.08100/) (2021)
- [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)
- [Generative Restricted Kernel Machines: A Framework for Multi-view Generation and Disentangled Feature Learning](https://mlsanity.com/paper/1906.08144/) (2019)
- [Boltzmann machines and energy-based models](https://mlsanity.com/paper/1708.06008/) (2017)
- [Robust Generative Restricted Kernel Machines using Weighted Conjugate Feature Duality](https://mlsanity.com/paper/2002.01180/) (2020)
- [Latent Space Exploration Using Generative Kernel PCA](https://mlsanity.com/paper/2105.13949/) (2021)
- [Boltzmann machines for time-series](https://mlsanity.com/paper/1708.06004/) (2017)

## Built on by (most cited first, 2 of 2)

- [Duality in Multi-View Restricted Kernel Machines](https://mlsanity.com/paper/2305.17251/) (2023)
- [KROM: Kernelized Reduced Order Modeling](https://mlsanity.com/paper/2603.00360/) (2026)

## Abstract (arXiv)

In this paper, we propose a kernel principal component analysis model for multi-variate time series forecasting, where the training and prediction schemes are derived from the multi-view formulation of Restricted Kernel Machines. The training problem is simply an eigenvalue decomposition of the summation of two kernel matrices corresponding to the views of the input and output data. When a linear kernel is used for the output view, it is shown that the forecasting equation takes the form of kernel ridge regression. When that kernel is non-linear, a pre-image problem has to be solved to forecast a point in the input space. We evaluate the model on several standard time series datasets, perform ablation studies, benchmark with closely related models and discuss its results.