Scaled Cross Distance Minimization Algorithm And Its Application In Imbalanced Classification

The geometry support vector machine is a method that uses the geometric information of the sample set to find the solution.It has the advantages of simple and intuitive geometric features and high calculation accuracy.In the case of linear separability,the maximum interval classification hyperplane can be solved by solving for the nearest point between two convex hulls.When the dataset is non-linearly separable,appropriate convex hull scaling is required.Among them,scaled is a effective convex hull scaling method,which is less computationally complex than reduced convex hulls.However,the existing scaled nearest point algorithms have disadvantages such as insufficient iteration methods and slow running speed.Therefore,this paper proposes a new scaled nearest point algorithm,based on the cross distance minimization algorithm,and has done the following two tasks:(1)Propose a scaled cross distance minimization algorithm to solve non-linear separable problem.The scaled cross distance minimization algorithm is to first use the scaled convex hull methods to apply the method of scaled convex hulls to make the two intersecting convex hulls in the nonlinear separable case separable,and then use the cross kernel distance minimization algorithm to solve the nearest point pair to construct the maximum interval classification hyperplane.Compared with the existing scaled nearest point algorithm,the method in this paper updates the nearest point pair at the same time,the convergence speed is faster and the implementation is simpler.Experimental results show that this method has a faster convergence rate and a simpler classification model under the premise of ensuring the classification accuracy.(2)A single-type convex hull scaled mechanism is proposed to solve the problem of imbalanced classificationIn the problem of imbalanced classification,the classification plane obtained by traditional classifier tends to tilt toward the convex hull generated by the minority samples,making the minority samples misclassified.However,in many studies we need more feature information of the minority samples,which is contrary to the result we need.Therefore,this paper proposes a single-class convex hull scaled mechanism,which gives the convex hull of most classes a smaller scaling factor,but does not scale the convex hull formed by the minority class to show the importance of the minority class.In this way,the classification plane is far away from the minority samples and avoids the occurrence of misclassification of the minority samples.This method is similar to a under-sampling method,but does not delete or add sample data,so it avoids the loss of important data and the problem of data overfitting.The experimental results on the standard imbalanced dataset show that the performance of the classifier constructed by this method is better than other under-sampling methods.The performance of the proposed classifier is more outstanding when the two types of data in the imbalanced data set are more imbalanced.