In SVMs the polynomial kernel is defined as:
(scale * crossprod(x, y) + offset)^degree
How do the scale and offset parameters affect the model and what range should they be in? (intuitively please)
Are the scale and offset for numeric stability only (that's what it looks like to me), or do they influence prediction accuracy as well?
Can good values for scale and offset be calculated/estimated when the data is known or is a grid search required? The caret package always sets the offset to 1, but it does a grid search for scale. (Why) is an offset of 1 a good value?
PS.: Wikipedia didn't really help my understanding:
For degree-d polynomials, the polynomial kernel is defined as
where x and y are vectors in the input space, i.e. vectors of features computed from training or test samples, is a constant trading off the influence of higher-order versus lower-order terms in the polynomial. When , the kernel is called homogeneous.(A further generalized polykernel divides by a user-specified scalar parameter .)
Neither did ?polydot's explanation in R's help system:
scale: The scaling parameter of the polynomial and tangent kernel is a convenient way of normalizing patterns (<-!?) without the need to modify the data itself
offset: The offset used in a polynomial or hyperbolic tangent kernel (<- lol thanks)