If we could calculate the dot products from xz and x2 directly without considering the vectors ~(xz) and ¢(x2) projected onto the higher-dimensional space, we can reduce the computational complexity considerably.
namely, we can reduce the computational overhead if we could find the function K that satisfies: since we do not need itself for actual learning and classification, 1In general, ,It(x) is a mapping into Hilbert space.