If one does say "Kernel Ridge Regression" or "Kernel PCA" using the Gaussian kernel then do we know how the choice of the width of the Gaussian kernel affects the quality of the answer?

Like does in some provable sense the answer so obtained get increasingly "useless" as one keeps increasing the Gaussian width?

Very specifically : Do we know if the RKHS at two different Gaussian widths are isomorphic or not as function spaces?

  • $\begingroup$ It's a good idea to spell out abbreviations like RKHS the first time you use them. This is partly for the ease of readers who are unfamiliar with the term, but also so that people who search for the term in its unabbreviated form will still find your post. $\endgroup$ – Silverfish Aug 27 '16 at 0:57

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