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2.4.3 Common kernel functions

The kernel function needs to be a scalar product in some feature space. A sufficient condition is that the kernel matrix is positive semidefinite (Schölkopf et al., 1998b; Schölkopf and Smola, 2002, p. 44). Some common kernel functions that fulfill this condition are the polynomial kernel,

with a constant integer *d*, the Gaussian kernel,

with a constant
> 0, and the inverse multiquadric kernel,

with a constant *c* > 0 (Schölkopf and Smola, 2002, p. 54). The last two functions result in a kernel matrix with full rank (Micchelli, 1986). That is, all eigenvectors are linearly independent. Thus, the dimensionality of the feature space is not restricted (it is infinite).

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*Heiko Hoffmann *

2005-03-22