Kernel Function

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A Kernel Function is a distance function that evaluates the similarity between two structures (in some metric space).


  • tbd
    • If X is the instance space, a kernel function is a mapping K:XxX->[0,infinity) such that given two instances [math]x[/math] and [math]y[/math], K(x,y) = SUM(i) ti(x) ti(y) = t(x)·t(y), where ti(x) is some feature function over the instance x.




  • (Mitchell, 1997) ⇒ Tom M. Mitchell. (1997). “Machine Learning." McGraw-Hill.
    • Much of the literature on nearest-neighbor methods and weighted local regression uses a terminology that has arisen from the field of statistical pattern recognition....
      • Regression means approximating a real-valued target function.
      • Residual is the error f^(x) - [math]f[/math](x) in approximating the target function.
      • Kernel function is the function of distance that is used to determine the weight of each training example. In other words, the kernel function is the function [math]K[/math] such that wi = K(d(xi, xq)).