Transductive Inference Based Multi Dimensional Neville Algorithm for Estimating Values of Functions

doi:10.7523/j.issn.2095-6134.2005.1.010

Abstract

Abstract:

An algorithm based on transductive inference learning used for estimating values of functions .It does not use any predefined modules and parameters and estimates the values of functions directly .It is the biggest difference between traditional algorithms for estimating values of functions .But the most trouble is how to implement the algorithm.Our paper discusses a transductive inference based multi dimensional Neville algorithm for estimating values of functions .By the use of projecting methods , we get multi dimensional Neville algorithm for estimating values of functions .The results of experiments show our algorithm not only successfully overcomes Runge problem of traditional algorithm for estimating values of functions , but also has a very nice function values estimating results and can be used in multi dimensional circumstance .We also provide some discussion of the selection of kernel parameters .Our algorithm shows a brand new way in transductive inference field .

Key words: transductive inference, kernel function, function value estimating, Neville algorithm

CLC Number:

TP311

Ma Lin, Ye Shiwei, Luo Tiejian, Song Jinliang. Transductive Inference Based Multi Dimensional Neville Algorithm for Estimating Values of Functions[J]. , 2005, 22(1): 64-71.

References

[1] Vapnik V .The nature of statist ical learning theory .Springer , 1995

[2] Vapnik V .Statistical learning theory .John Wiley and Sons , 1998

[3] Gammerman A , Vapnik V , Vowk V.Learning by transduction .In :Proceedings of the 14th Conf erence on Uncertainty in Artifical Intelligence .Wisconsin , 1998 .148—156

[4] Joachims T.Transductive inference for text classificat ion using support vector machine .In :Proceedings of the 16th International Conference onMachine Learning (ICML).San Francisco :Morgan Kaufmann Publishers , 1999 .200—209

[5] Chen YS , Wang GP, Dong SH .A progressive transductive inference algorithm based on support vector machine .Journal of Software .2003 , 14(3):451—460(in Chinese with English abstract)

[6] Chapelle O, Vapnik V, Weston J .Transductive inference for estimating values of functions .　http : axiom .anu .edu .au—manoji t SVM Papers %20and %20Articles ChapelleVapnikWeston .ps

[7] Li QY, Wang NC , Yi DL.Numerical analysis .Wuhan :Huazhong University of Science and Technology (HUST)Press ,1982(in Chinese)

[8] Yang PF , Zhang CS .Artificial neutral network and simulated evolutionary computing .Beijing:Tsinghua University Press, 1999(in Chinese)

[9] Yuan YX, Sun WY .Optimization theory and method .Bei jing:Science Press , 1997(in Chinese)

[10] Graepel T, Herbri ch R, Obermayer K .http : axiom.anu .edu .au—manojit SVM Papers %20and %20Arti cles graeherober99b .ps

附中文参考文献

[5] 陈毅松, 汪国平, 董士海.基于支持向量机的渐进直推式分类学习算法.软件学报,2003 , 14(3):451—460

[7] 李庆扬, 王能超, 易大义.数值分析.武汉:华中科技大学出版社, 1982

[8] 阎平凡, 张长水.人工神经网络与模拟进化计算.北京:清华大学出版社,1999

[9] 袁亚湘, 孙文瑜.最优化理论与方法.北京:科学出版社, 1997