On the Convergence of Eigenspaces in Kernel Principal Component
Laurent Zwald and Gilles Blanchard
In: NIPS 2005, 5-8 Dec 2005, Vancouver.
This paper presents a non-asymptotic statistical analysis of Kernel-PCA with a
focus different from the one proposed in previous work on this topic.
Here instead of considering the reconstruction error of KPCA
we are interested in approximation error bounds for
the eigenspaces themselves. We prove an upper bound depending on the spacing between eigenvalues but not
on the dimensionality of the eigenspace.
As a consequence this allows to infer stability results for
these estimated spaces.