Deep Hyper Sphere Support Vector Machine

Anomaly detection is a kind of task to detect the data that deviates from most data observations.The deep mixture model has a good performance in the current anomaly detection task.However,due to the theoretical property of the shallow model,the existing deep mixing model lacks the exact solution method.This seriously affects the classification performance and solving speed of these deeply mixed models.To solve the above problems,this paper proposes complete deep hypersphere one class support vector data description(CDH-SVDD)and complete deep hypersphere multi-class support vector data description(CDHMC-SVDD),two deep hybrid models.It is suitable for single-peak distribution and multi-peak distribution of normal data.In this paper,it is collectively referred to as deep hypersphere support vector machine(DH-SVM).This model has a precise solution algorithm,which can have more powerful classification performance and faster solving speed.In this paper,ν-SVDD is improved and an improved ν-SVDD model is proposed for the case of single-peak distribution of normal data.The optimization problem corresponding to the improved model is convex and satisfies strong duality,which makes the model parameters can be solved accurately after the introduction of neural network.Then,based on the improved model of ν-SVDD,this paper proposes CDH-SVDD and its exact solving algorithm,and proves the upper-lower bound properties of the super parameter ν.In this paper,the comparative experimental results of 5 models on 7 data sets such as CIFAR-10 show that CDH-SVDD usually has higher AUC value and F1 score than other models.At the same time,CDH-SVDD usually has higher convergence speed and solving speed than other deep mixing models.In view of the multi-peak distribution of normal data,this paper improves MSSVDD and proposes an improved model of MS-SVDD.The improved model solves the problem that the optimization problem corresponding to the original model is not convex and the strong duality cannot be guaranteed.This makes the parameters of the model can be solved accurately after the introduction of neural network.Then,based on the improved model of MS-SVDD,CDHMC-SVDD and its exact solution algorithm are proposed,and the upper-lower bound properties of the super parameterν are proved.In this paper,the experimental results of comparison with 7 models on 3 data sets,such as MNIST,show that CDHMC-SVDD usually has higher AUC value than other models.At the same time,the convergence rate of this model is significantly faster than that of other deep mixing models,which makes up for the time spent in solving convex optimization problems during parameter updating of this model.Even if all data sets are required when model parameters are updated,the solution speed of CDHMC-SVDD is not significantly different from that of other models.