# Kernel Function

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

## References

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

### 1997

• (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) - $f$(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 $K$ such that wi = K(d(xi, xq)).