In the practical learning process, only the inner products of the feature vectors are needed (see Section 2.2, 2.3 and 3), so we can perform the so-called kernel trick to avoid dealing with the very highdimensional feature vectors explicitly.
for x, z ∈ X , a kernel function is defined as: In our case, the blended n-spectrum string kernel (Lodhi et al., 2002) that compares two strings by counting how many (contiguous) substrings of length from 1 up to n they have in common, is a good choice for the kernel function to induce our feature spaces H x and H y implicitly, even though it brings in some uninformative features (word n-grams) as well, when compared to our original definition.