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