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Kernel PCA and the Nyström method

Hallgren, Fredrik; (2022) Kernel PCA and the Nyström method. Doctoral thesis (Ph.D), UCL ( University College London). Green open access

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Abstract

This thesis treats kernel PCA and the Nystrom method. We present a novel incre- ¨ mental algorithm for calculation of kernel PCA, which we extend to incremental calculation of the Nystrom approximation. We suggest a new data-dependent ¨ method to select the number of data points to include in the Nystrom subset, ¨ and create a statistical hypothesis test for the same purpose. We further present a cross-validation procedure for kernel PCA to select the number of principal components to retain. Finally, we derive kernel PCA with the Nystrom method ¨ in line with linear PCA and study its statistical accuracy through a confidence bound.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Kernel PCA and the Nyström method
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10148112
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