Formally, the kernel is a function k : X × X → R that takes as input two data objects (e.g., vectors, texts, parse trees) and outputs a real number characterizing their similarity, with the property that the function is symmetric and positive semi-definite.
for all where φ is an explicit mapping from X to an (inner product) feature space F. In the next sections, we define and combine different kernel functions that calculate the pairwise similarly between multi-contexts.