The structured margin is defined in terms of a score function S : X × Y → , in our case the linear score function S(x, y) = w T Φ(x, y), where w ∈ m is a vector of parameters and Φ : X ×Y → m is a joint feature function.
the learning problem then amounts to finding parameters w such that S(x, y x ) ≥ S(x, y) + ∆(y x , y) for all y ∈ Y x \ {y x } over the training data D. we want the score of the correct label to be higher than the score plus the loss, of all other labels, for each instance.