UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Upper and Lower Bounds on the Performance of Kernel PCA.

Haddouche, M; Guedj, B; Rivasplata, O; Shawe-Taylor, J; (2020) Upper and Lower Bounds on the Performance of Kernel PCA. arXiv: Ithaca, NY, USA. Green open access

[thumbnail of 2012.10369v1.pdf]
Preview
Text
2012.10369v1.pdf - Accepted version

Download (510kB) | Preview

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
Downloads since deposit
7Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item