mlsanityData to 7 Oct 2026

Kernel PCA with the Nystr"om method

arXiv 2109.05578 ↗First posted 12 Sep 2021stat.ML cs.LG math.STcited by 2

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Abstract (arXiv)

The Nystr"om method is one of the most popular techniques for improving the scalability of kernel methods. However, it has not yet been derived for kernel PCA in line with classical PCA. In this paper we derive kernel PCA with the Nystr"om method, thereby providing one of the few available options to make kernel PCA scalable. We further study its statistical accuracy through a finite-sample confidence bound on the empirical reconstruction error compared to the full method. The behaviours of the method and bound are illustrated through computer experiments on multiple real-world datasets. As an application of the method we present kernel principal component regression with the Nystr"om method, as an alternative to Nystr"om kernel ridge regression for efficient regularized regression with kernels.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 17 of its 102 references that are in the map. First posted on arXiv 12 Sep 2021.

Builds on

17 of 102 references.

References · 17

  1. 2018Just Interpolate: Kernel "Ridgeless" Regression Can Generalizecited by 190
  2. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  3. 2019A Primer on PAC-Bayesian Learningcited by 130
  4. 2019Kernel Instrumental Variable Regressioncited by 118
  5. 2015Less is More: Nystr"om Computational Regularizationcited by 89
  6. 2020Kernel methods through the roof: handling billions of points efficientlycited by 88
  7. 2017FALKON: An Optimal Large Scale Kernel Methodcited by 82
  8. 2013Revisiting the Nystrom Method for Improved Large-Scale Machine Learningcited by 76
  9. 2017Diving into the shallows: a computational perspective on large-scale shallow learningcited by 30
  10. 2014Statistical and computational trade-offs in estimation of sparse principal componentscited by 26
  11. 2021Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processescited by 17
  12. 2021Statistical Optimality and Computational Efficiency of Nystr"om Kernel PCAcited by 10
5 more
  1. 2017Approximate Kernel PCA Using Random Features: Computational vs. Statistical Trade-offcited by 8
  2. 2014Metric and non-metric proximity transformations at linear costscited by 5
  3. 2015Linearized Kernel Dictionary Learningcited by 5
  4. 2021ParK: Sound and Efficient Kernel Ridge Regression by Feature Space Partitionscited by 5
  5. 2020Upper and Lower Bounds on the Performance of Kernel PCAcited by 3

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Citing papers per year: 2025: 2.

2 papers.

  1. 2025Autoencoding Random Forestscited by 3
  2. 2025Kernel PCA for Out-of-Distribution Detection: Non-Linear Kernel Selection and Approximationcited by 1