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Exploiting low-rank approximations of kernel matrics in denoising applicationS
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The eigendecomposition of a kernel matrix can present a
computational burden in many kernel methods. Nevertheless
only the largest eigenvalues and corresponding eigenvectors
need to be computed. In this work we discuss the
Nystrom low-rank approximations of the kernel matrix and
its applications in KPCA denoising tasks. Furthermore, the
low-rank approximations have the advantage of being related
with a smaller subset of the training data which constitute
then a basis of a subspace. In a common algebraic
framework we discuss the different approaches to compute
the basis. Numerical simulations concerning the denoising
are presented to compare the discussed approaches.