Local optimisation of Nystr\"om samples through stochastic gradient descent

• URL: http://arxiv.org/abs/2203.13284v1
• Date: Thu, 24 Mar 2022 18:17:27 GMT
• Title: Local optimisation of Nystr\"om samples through stochastic gradient descent
• Authors: Matthew Hutchings and Bertrand Gauthier
• Abstract summary: We consider an unweighted variation of the squared-kernel discrepancy criterion as a surrogate for the classical criteria used to assess the Nystr"om approximation accuracy. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nystr"om samples with improved Nystr"om approximation accuracy.
• Score: 32.53634754382956
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a relaxed version of the column-sampling problem for the Nystr\"om approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nystr\"om samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nystr\"om approximation accuracy; in this setting, we discuss how Nystr\"om samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nystr\"om samples with improved Nystr\"om approximation accuracy.

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