Haddouche, M;
Guedj, B;
Rivasplata, O;
Shawe-Taylor, J;
(2020)
Upper and Lower Bounds on the Performance of Kernel PCA.
arXiv: Ithaca, NY, USA.
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Abstract
Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. Recently, kernel PCA has emerged as an extension of PCA but, despite its use in practice, a sound theoretical understanding of kernel PCA is missing. In this paper, we contribute lower and upper bounds on the efficiency of kernel PCA, involving the empirical eigenvalues of the kernel Gram matrix. Two bounds are for fixed estimators, and two are for randomized estimators through the PAC-Bayes theory. We control how much information is captured by kernel PCA on average, and we dissect the bounds to highlight strengths and limitations of the kernel PCA algorithm. Therefore, we contribute to the better understanding of kernel PCA. Our bounds are briefly illustrated on a toy numerical example
| Type: | Working / discussion paper |
|---|---|
| Title: | Upper and Lower Bounds on the Performance of Kernel PCA. |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://arxiv.org/abs/2012.10369v1 |
| Language: | English |
| Additional information: | CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Statistical learning theory, kernel PCA, PAC-Bayes, dimension reduction. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science 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 Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10118216 |
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