Exploiting Low-Rank Approximations of Kernel Matrices in Denoising Applications

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 Ny strm 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.