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Wikipediaorgwikik nearestneighborsalgorithm 28 7

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Unformatted text preview: nce can be expressed in terms of dot products: Dis 2 (x, y) = ||x y||2 = p (x y )| (x Replacing dot products with kernels: p Dis K (x, y) = K (x, x) y) = p 2K (x, y) x| x 2x| y Replacing dot products with kernels: Dis K (x, y) = y| y p K (x, x) 2K (x, y) K (y , y ) If we consider a kernel that satisfies K(x,x) = 1, then nearest neighbor classification with kernels or distances is equivalent. K (y , y ) As an alternative, consider kernels as measures of similarity, and rather than looking for the closest points, look for the most similar points, and use kernels directly. 29 30 8...
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