一种基于训练数据的迭代改进核函数
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摘要
为提高支持向量机性能,提出一种支持向量机核函数的迭代改进新算法.利用与数据有关的保角映射,使核函数包含了全部学习样本的信息,即核函数具有数据依赖性.基本核函数的参数可取随机初值,通过对核函数进行多次迭代改进,直至得到满意的学习效果.与传统方法相比,新算法不需要筛选核函数的参数.对一元连续函数和强地震事件的仿真计算结果表明,改进SVR(support vector regression)的学习效果优于传统方法,并且随着迭代次数的增加,学习风险下降收敛,收敛速度依赖于传统方法的基本参数和改进方法的参数.
In order to improve the performance of a support vector regression,a new method for modified kernel function is proposed.In this method the information of whole samples is included in kernel function by conformal mapping.So the kernel function is data-dependent.With random initial parameter of kernel function,the kernel function is modified repeatedly until a satisfactory effect is achieved.Compared with the conventional model,the improved approach needs not selecting parameters of kernel function.Simulation was finished for one-dimension continue function and strong earthquake event.The results show that the improved approach has better learning ability and forecasting precision than the traditional model.With the iteration number increasing,the figure of merit will decrease and converge.The speed of convergence depends on the parameters in the algorithm.
In order to improve the performance of a support vector regression,a new method for modified kernel function is proposed.In this method the information of whole samples is included in kernel function by conformal mapping.So the kernel function is data-dependent.With random initial parameter of kernel function,the kernel function is modified repeatedly until a satisfactory effect is achieved.Compared with the conventional model,the improved approach needs not selecting parameters of kernel function.Simulation was finished for one-dimension continue function and strong earthquake event.The results show that the improved approach has better learning ability and forecasting precision than the traditional model.With the iteration number increasing,the figure of merit will decrease and converge.The speed of convergence depends on the parameters in the algorithm.
引文
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[9]Amari S,Wu Si.Improving support vector machine classifiers by modifying kernel functions[J].Neural Networks,1999,12(6):783-789.
[10]LIANG Yan-chun,SUN Yan-feng.An improved method of support vector machine and its applica-tions to financial time series forcesting[J].Progresss in Natural Science,2003,13(9):696-700.
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[12]马润勇,彭建兵.震级与破裂尺度及位错量关系的讨论[J].西北大学学报(自然科学版),2006,36(5):799-802.
[2]Scholkopf B,Sung K,Burges C.Comparing support vector machines with Gaussian kernels to radialbasis function classifiers[J].IEEE Trans Signal Processing,1997,45(11):2758-2765.
[3]Perez-Cruz F,Navia-Vazquez A,Figueiras-Vidal A R,et al.Empirical risk minimization for supportvector classifiers[J].IEEE Trans on Neural Networks,2003,14(2):296-303.
[4]Belhumeur P N,Hespanha J P,Kriegman D J.Eigenfaces vs Fisherfaces:Recognition using classspecific linear projection[J].IEEE Trans on Pattern Analysis and Machine Intelligence,1997,19(7):711-720.
[5]CAO Li-juan,Tay Francis E H.Financial forecasting using support vector machines[J].NeuralComputing&Applications,2001,10(2):184-192.
[6]Tay Francis E H,CAO Li-juan.-εDescending support vector machines for financial time series fore-casting[J].Neural Processing Letters,2002,15(2):179-195.
[7]YANG Hai-qin,CHAN Lai-wan,King Irwin.Support vector machine regression for volatile stockmarket prediction[A].In:Yin H,Allinson N,Freeman R,et al,Eds.Proceedings of Intelligent Da-ta Engineering and Automated Learning[C].Berlin:Springer-Verlag,2002.319-396.
[8]Smola A J,Sch lkopf B,M Ller K R.The connection between regularization operators and supportvector kernels[J].Neural Network,1998,11(4):637-649.
[9]Amari S,Wu Si.Improving support vector machine classifiers by modifying kernel functions[J].Neural Networks,1999,12(6):783-789.
[10]LIANG Yan-chun,SUN Yan-feng.An improved method of support vector machine and its applica-tions to financial time series forcesting[J].Progresss in Natural Science,2003,13(9):696-700.
[11]Colin C.Kernel methods:a survey of current techniques[J].Neurocomputing,2002,48:63-84.
[12]马润勇,彭建兵.震级与破裂尺度及位错量关系的讨论[J].西北大学学报(自然科学版),2006,36(5):799-802.
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