Yes in principle just compute them no need to modify

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Unformatted text preview: Fine print: if your kernel doesn’t sa)sfy certain technical requirements, lots of proofs break. E.g. convergence, mistake bounds. In prac)ce, illegal kernels some%mes work (but not always). Non ­Linearity Non ­Linear Separators   Data that is linearly separable works out great for linear decision rules: x 0   But what are we going to do if the dataset is just too hard? x 0   How about… mapping data to a higher ­dimensional space: x2 0 x This and next few slides adapted from Ray Mooney, UT Non ­Linear Separators   General idea: the original feature space can always be mapped to some higher ­ dimensional feature space where the training set is separable: Φ: x → φ(x) Why Kernels?   Can’t you just add these features on your own (e.g. add all pairs of features instead of using the quadra)c kernel)?         Yes, in principle, just compute them No need to modify any algorithms But, number of features can get large (or infinite) S...
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This note was uploaded on 12/22/2013 for the course CS 188 taught by Professor Staff during the Fall '08 term at University of California, Berkeley.

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