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Sep 26, 2014 at 4:17 comment added Aaron I believe you are correct that the kernel function doesn't need to map into a higher dimensional space. However, in practice the popular kernel functions (polynomial kernels, rbf kernel, ...) do map into higher dimensions. This is the whole purpose of the kernel trick.
Sep 26, 2014 at 4:10 comment added InformedA I don't think the kernel function maps input into higher dimensional space. What the kernel function does is mapping input into another space that will be homeomorphic to the original one
Sep 26, 2014 at 1:00 history edited D.W. CC BY-SA 3.0
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Sep 25, 2014 at 22:55 history answered Aaron CC BY-SA 3.0