Here α i are Lagrangian multipliers and K(x,y)=⟨ϕ(x),ϕ(y)⟩ is a kernel function. The process of solving the optimization problem is known as training the SVM and using the SVM to classify new data is known as testing. The parameter C controls the tradeoff between minimization of training error and maximization of generalization capability. The separating hyperplane is usually written in terms of the Lagrangian Multipliers as