| 引用本文: | 王建建,何枫,吴子轩,陈丽莉.Pad′e32光滑支持向量机模型的构造及其应用[J].控制理论与应用,2018,35(9):1302~1310.[点击复制] |
| WANG Jian-jian,HE Feng,WU Zi-xuan,CHEN Li-li.Construction of Pad′e32 smooth support vector machine model and its application[J].Control Theory and Technology,2018,35(9):1302~1310.[点击复制] |
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| Pad′e32光滑支持向量机模型的构造及其应用 |
| Construction of Pad′e32 smooth support vector machine model and its application |
| 摘要点击 2397 全文点击 906 投稿时间：2017-12-18 修订日期：2018-09-19 |
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| DOI编号 10.7641/CTA.2018.70941 |
| 2018,35(9):1302-1310 |
| 中文关键词 机器学习 光滑支持向量机模型 Pad′e32光滑函数 分类 BFGS–Armijo算法 |
| 英文关键词 machine learning smooth support vector machine Pad′e32 smooth function classification BFGS–Armijo algorithm |
| 基金项目 国家自然科学基金项目(71673022,71701016), 北京市自然科学基金项目(9174038), 北京社会科学基金项目(17LJB004), 中央高校基本科研业务费 用项目(FRF-0T-17-018). |
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| 中文摘要 |
| 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Pad′e32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Pad′e32–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. |
| 英文摘要 |
| 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. |
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