Given the optimizer α α α for the dual problem, the resulting sphere (and decision rule) can be expressed in terms of only the support vectors-those training response vectors with α i > 0. The support vectors lie either on the sphere (0 < α i < C) or outside of it (α i = C). The decision rule in eqn. 5 in terms of α α α and the kernel of the test response vector m with the support vectors is: