The constrained primal of the support vector machine can be rewritten as an unconstrained loss-plus-penalty objective: a sum of hinge losses, (1 - y f(x))_+, plus a lambda-weighted squared L2 norm of the weight vector. In this reading the margin constraints become the loss term enforcing correct classification with a margin, while the norm term that originally defined the margin becomes the regularization penalty, making the SVM structurally identical to ridge regression with the squared loss replaced by the hinge loss. This places the SVM within the general regularized empirical risk minimization framework of statistical machine learning, where different surrogate convex losses — hinge, squared, and logistic — are chosen as tractable substitutes for the non-convex 0-1 loss that classification actually targets.
The constrained primal of the support vector machine can be rewritten as an unconstrained loss-plus-penalty objective: a sum of hinge losses, (1 - y f(x))_+, plus a lambda-weighted squared L2 norm of…