Support vector machine

The support vector machine (SVM)^29–31, one of the dominant statistical learning algorithms was adopted as a core prediction algorithm. It seeks the optimum hyperplane with the highest margin between two groups^18,40. Furthermore, it solves the problem of constraint optimization as described below

Subject to: ∑i=1nyiαi=0,0≤αi≤C, for all i=1,2,3,...,n. After involving the kernel function, the discriminant function of SVM took the following form

In this paper, the radial basis function kernel^18,41 was applied to construct SVM classifier and given by, k(xi,xj)=exp(-γ‖xi-xj‖2), where γ>0⁴². As the benchmark dataset was highly imbalanced, different error cost (DEC)¹⁸ method had been used to tackle the class imbalance problem^24,43. According to this approach, the SVM soft margin objective function was adjusted to allocate two costs for misclassification¹², such as C+ for the positive class instances and C- for the negative class instances

In Eq. (¹⁶), W+ is the weight for the positive instances and W- is the weight for the negative instances and defined by

 W+=M2∗M1,W-=M2∗M2 where M is the total number of elements, M1 is the number of elements for the positive class, and M2 is the number of elements for the negative class.