基于岭惩罚与修正的SCAD惩罚的软间隔SVM分类模型与算法及其应用

Soft Margin SVM Classification Model and Algorithm Based on Ridge Penalty and Modified SCAD Penalty and Its Applications

摘要: 基于岭惩罚与传统的SCAD惩罚的软间隔SVM分类算法已成功应用于医学诊断等领域。然而传统的SCAD惩罚只考虑样本信息的影响，未考虑到先验信息的影响，故此，基于岭惩罚与传统的SCAD惩罚的软间隔SVM分类算法有一定的局限性。修正的SCAD惩罚同时考虑了样本信息与先验信息的影响，是传统的SCAD惩罚的重要拓广，目前未发现基于岭惩罚与修正的SCAD惩罚的软间隔SVM分类算法的研究。基于此，本文首先将岭惩罚与修正的SCAD惩罚相结合，并与软间隔SVM分类算法融合，构建基于岭惩罚与修正的SCAD惩罚的软间隔SVM分类模型。然后，引入AIC和BIC信息准则求解参数。最后，通过心脏病诊断实例验证了所提模型与算法具有更高的灵敏度、特异度和分类能力。

Abstract: Soft margin SVM classification algorithms based on ridge penalty and traditional SCAD penalty have been successfully applied in fields such as medical diagnosis. However, traditional SCAD penalty only considers the influence of the sample information and does not take into account the influence of prior information. Therefore, soft margin SVM classification algorithms based on ridge penalty and traditional SCAD penalty have certain limitations. The modified SCAD penalty simultaneously considers the influence of both the sample information and prior information, representing an important extension of the traditional SCAD penalty. To date, no research has been found on soft margin SVM classification algorithms based on ridge penalty and modified SCAD penalty. Based on this, this paper first combines ridge penalty with modified SCAD penalty and integrates them with the soft margin SVM classification algorithm to construct a soft margin SVM classification model based on ridge penalty and modified SCAD penalty. Then, AIC and BIC information criteria are introduced to solve the parameters. Finally, the proposed algorithm is validated through a cardiac diagnosis example, demonstrating higher sensitivity, specificity, and classification capability.