eprintid: 1712
rev_number: 6
eprint_status: archive
userid: 46
dir: disk0/00/00/17/12
datestamp: 2013-09-13 09:51:09
lastmod: 2013-09-16 12:03:00
status_changed: 2013-09-13 09:51:09
type: article
metadata_visibility: no_search
creators_name: Gnecco, Giorgio
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
title: Accuracy of suboptimal solutions to kernel principal component analysis
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Principal component analysis (PCA); Kernel methods; Suboptimal solutions; Primal and dual problems; Lagrangian; Regularized optimization problems
abstract: For Principal Component Analysis in Reproducing Kernel Hilbert Spaces (KPCA), optimization over sets containing only linear combinations of all n-tuples of kernel functions is investigated, where n is a positive integer smaller than the number of data. Upper bounds on the accuracy in approximating the optimal solution, achievable without restrictions on the number of kernel functions, are derived. The rates of decrease of the upper bounds for increasing number n of kernel functions are given by the summation of two terms, one proportional to n −1/2 and the other to n −1, and depend on the maximum eigenvalue of the Gram matrix of the kernel with respect to the data. Primal and dual formulations of KPCA are considered. The estimates provide insights into the effectiveness of sparse KPCA techniques, aimed at reducing the computational costs of expansions in terms of kernel units. 
date: 2009
date_type: published
publication: Computational Optimization and Applications
volume: 42
number: 2
publisher: Springer
pagerange: 265-287
id_number: 10.1007/s10589-007-9108-y
refereed: TRUE
issn: 0926-6003
official_url: http://dx.doi.org/10.1007/s10589-007-9108-y
citation:   Gnecco, Giorgio and Sanguineti, Marcello  Accuracy of suboptimal solutions to kernel principal component analysis.  Computational Optimization and Applications, 42 (2).  pp. 265-287.  ISSN 0926-6003      (2009)