Error bounds for suboptimal solutions to kernel principal component analysis

摘要

Suboptimal solutions to kernel principal component analysis are considered. Such solutions take on the form of linear combinations of all n-tuples of kernel functions centered on the data, where n is a positive integer smaller than the cardinality m of the data sample. Their accuracy in approximating the optimal solution, obtained in general for n = m, is estimated. The analysis made in Gnecco and Sanguineti (Comput Optim Appl 42:265–287, 2009) is extended. The estimates derived thereinfor the approximation of the first principal axis are improved and extensions to the successive principal axes are derived.