Padé32光滑支持向量机模型的构造及其应用

Construction of Padé32 smooth support vector machine model and its application

含无约束条件支持向量机的目标函数具有不光滑性,使得研究者难以采用快速的最优化算法对其进行求解.为了克服支持向量机的不可微性,文章首先应用有理逼近的方法,提出了一种新的Padé32逼近式光滑函数并建立了基于该函数的光滑支持向量机模型.其次,分析并证明了新光滑函数的逼近精度均高于已有的各种光滑函数,以及新模型的收敛性.最后,基于UCI机器学习数据库,将本文构造的Padé32–SSVM模型应用于若干种疾病的诊断、钞票验伪和生物可降解性分析中,结果表明本文建立的新光滑支持向量机模型具有较高的分类精度.

The objective function of support vector machine(SVM)without constraints is non-smooth,which makes it difficult to solve problems with optimization algorithm.To overcome non-smooth property of this model,a new Pad′e32 approximation smooth function is proposed,based on rational approximation method.Then,a new SSVM based on Pad′e32 smooth function is established.Theoretical analysis proved that the smooth precision is significantly higher than existing smooth functions.Moreover,theorem proof is given to demonstrate the convergence of the new model.Finally,based on the UCI machine learning database,the Pad′e32–SSVM model is applied to the diagnosis of several diseases,banknote verification and biodegradability analysis.The results show that the new model has a high classification accuracy.