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- W3049398535 abstract "We explore the properties of the squared-kernel-discrepancy (SKD) framework for the Nystrom approximation of integral operators related to symmetric positive-semidefinite kernels. We describe how SKD-based approaches make use of the Hilbert-Schmidt geometry of the set of all trace-class integral operators defined form a given kernel and acting on the Hilbert space for which the kernel is reproducing. In this setting, we investigate the connections between SKD, spectral approximation and kernel approximation. We also describe how the properties of the conic SKD, a variation of the SKD invariant under rescaling of the approximate measures, can be combined with the notion of affine restriction to define sequential-type procedures for the design of sparse approximate measures corresponding to low-conic-SKD configurations; we in addition point out an interesting connection between conic-SKD minimisation and the search of specific low-energy configurations. The efficiency of the proposed sequential procedures is demonstrated on a series of examples, and the ability of SKD-based approaches to lead to accurate approximation of the main eigenpairs of very large kernel matrices is further illustrated." @default.
- W3049398535 created "2020-08-21" @default.
- W3049398535 creator A5063492396 @default.
- W3049398535 date "2020-08-24" @default.
- W3049398535 modified "2023-09-25" @default.
- W3049398535 title "Low-rank kernel approximation, Nyström method and conic squared-kernel discrepancy" @default.
- W3049398535 hasPublicationYear "2020" @default.
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