Consider binary label sample , where , . We assume that the optimal hyperplane separating data
pairs into binary classes is Relevant decision function is the
Heaviside step function For each data pair , the
geometric margin is defined as Since the confidence we have in the
separate hyperplane is positive proportional to the geometric margin,
then we define the geometric margin between the hyperplane and dataset as The
core implementation of SVM is to maximize the geometric margin, i.e. to
find If the minimum function margin
() is fixed to , then the preposition is equivalent to
Take Lagrange multiplier matrix ,then the
Lagrange function is The Lagrange dual problem gives We firstly consider internal
minimization, where Then the original function becomes The terminal target function is
Once the iteration has reached equilibrium state, denoted as , then we can solve the
corresponding parameters and , where