【作者】 周怡；

【导师】 万福永；

【作者基本信息】 华东师范大学 ， 应用数学， 2019， 硕士

【摘要】 机器学习主要是用来分析处理数据,挖掘数据背后所潜在的相关信息.大数据时代,如何准确快速地挖掘信息背后的关系已成为热点.支持向量机是由Vapnik等人提出的一项用于数据挖掘的新技术,主要用于模式识别、回归分析等方面.支持向量机的优点在于算法具有稀疏性,运算结果只受一部分样本的影响,抗干扰能力强.此外,通过加入正则项,支持向量机还能防止了“过拟合”.本文主要研究内容:(1)由最大间隔法推广所得的ε-支持向量回归机(ε-SVR)与结构风险最小化回归机(t-SVR)两者的内部联系.(2)文中简略介绍了ε-支持向量回归机、最小二乘法支持向量回归机(LSSVR),以及由ε-SVR算法变形出的v-支持向量回归机(v-SVR).此外,改进了v-SVR算法中的损失函数,分别得到了高斯损失支持向量回归机(GSVR)、混合损失支持向量回归机(MSVR),并用实际数据进行以上五种算法的性能评估.本文研究结论:(1)设ε-SVR算法在参数选定C时,所得的最优解为(w*(C),b*,ξ(*),此时若令t=‖w*(C)‖,则可验证(w*(C),b*)是t-SVR算法的一个最优解,两者等价.(2)无论线性还是非线性回归问题,GSVR算法、MSVR算法在参数C相同且v选取较大时,得到的回归函数与LSSVR算法等价,且对训练集的拟合效果都优于v-SVR算法;对于某些样本集,采用ε不敏感损失的ε-SVR算法性能比其他几种算法预测效果更好,且抗干扰能力更强.(3)对于多元非线性的问题,结合文中的两个实际问题,GSVR算法的预测能力较好。更多还原

【Abstract】 Machine learning is mainly used to analyze and process data,and to mine the potential relevant information of the data.In the era of big data,it’s a hot topic.to accurately and quickly mine the relations of the information.The Support Vector Machines is a new technology for data mining proposed by Vapnik.,mainly used in pattern recognition,regression analysis and other aspects.The sparsity of algorithm is the advantage of SVM.and the result of the algorithm is only affected by a part of samples,so SVM has strong anti-interference ability.In addition,the SVM algorithm can also prevent over-fitting by adding regularizationThe main researches content of this paper:(1)what the connection is between the ε-Support Vector Regression algorithm(ε-SVR)which is derived from the maximization margin method and the Structural Risk Minimization Regression algorithm(t-SVR)in statistics.(2)By improving the loss function of the v-Support Vector Regression machine(v-SVR),this paper proposes Gauss Loss Support Vector Regression algorithm(GSVR)and Mixed Loss Support Vector Regression algorithm(MSVR),and a comparative research among the ε-SVR、v-SVR、LSSVR、GSVR and MSVR with specific dataThe main conclusions of this paper:(1)If the optimal solution of the ε-SVR algorithm is(w*(C),b*,ξ(*)when the parameter C is determined and the parameter t of the t-SVR algorithm satisfies t=‖=w*(C)‖,then we can prove that these two algorithms are equivalent.(2)Both linear regression and nonlinear regression problems,when the parameter v of GSVR and MSVR approaches positive infinity,GSVR and MSVR are equivalent to LSSVR with the same C.In addition,according to the data experimental results,the regression results of training set get by ε-SVR、LSSVR、GSVR and MSVR algorithms are better than v-SVR algorithm.(3)For the nonlinear regression problems,combined with the two practical problems in this paper,the prediction ability of GSVR algorithm is better than others.更多还原