未确知支持向量机

杨志民; 邵元海; 梁静

doi:10.3724/SP.J.1004.2013.00895

未确知支持向量机

doi: 10.3724/SP.J.1004.2013.00895

1.
浙江工业大学之江学院杭州 310024;
2.
陕西煤业化工集团黄陵矿业有限公司黄陵 727307

基金项目:

国家自然科学基金(10926198, 11201426);浙江省自然科学基金(LQ 12A01020)资助

详细信息

通讯作者:
邵元海

计量
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- 被引次数: 0
出版历程
- 收稿日期: 2012-03-22
- 修回日期: 2012-10-31
- 刊出日期: 2013-06-20

Unascertained Support Vector Machine

1.
Zhijiang College, Zhejiang University of Technology, Hangzhou 310024;
2.
Shaanxi Coal Chemical Group, Huangling Mining Industry, Huangling 727307

Funds:

Supported by National Natural Science Foundation of China(10926198, 11201426) and the Zhejiang Provincial Natural Science Foundation of China(LQ12A01020)

摘要

摘要: 提出一种处理样本中含有未确知信息(一种不确定性信息)的支持向量机未确知支持向量机(Unascertained support vector machine, USVM)算法.首先,以未确知数学为基础,将含有未确知信息的分类问题转化为求解未确知机会约束规划问题.然后,将其转化为与其等价的二次规划. 据此给出未确知支持向量机.理论分析和试验结果均表明,该算法是有效、可行的.
- 机器学习 /
- 未确知支持向量机 /
- 未确知信息 /
- 未确知数
Abstract: In this paper, we propose an unascertained support vector machine (USVM) for classification problem with unascertained information (a kind of uncertain information). First, based on unascertained mathematics, classification problems containing unascertained information are converted to solving unascertained chance constrained programming problems. Then, the unascertained chance constrained programming is converted to its equivalent quadratic programming. Based on these theories, the algorithm of a unascertained support vector machine is given. Theoretical analysis and experiments show that the proposed USVM is effective and feasible.
- Machine learning /
- unascertained support vector machine (USVM) /
- unascertained information /
- unascertained number

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参考文献(26)

[1]	Wang Guang-Yuan. Unascertained information and its mathematical treatment. Journal of Harbin University of Civil Engineering and Architecture, 1990, 23(4): 1-9(王光远. 未确知信息及其数学处理. 哈尔滨建筑工程学院学报, 1990, 23(4): 1-9)
[2]	Liu Kai-Di, Wu He-Qin, Pang Yan-Jun. Mathematical Treatment and Application of Uncertain Information. Beijing: Science Press, 1999 (刘开第, 吴和琴, 庞彦军. 不确定性信息数学处理及应用. 北京: 科学出版社, 1999)
[3]	Yang Z M. Review of the monograph mathematical treatment and application of uncertain information. Chinese Science Bulletin, 2001, 46(7): 615-616
[4]	Liu Kai-Di, Cao Qing-Kui, Pang Yan-Jun. A method of fault diagnosis based on unascertained set. Acta Automatica Sinica, 2004, 30(5): 747-756(刘开第, 曹庆奎, 庞彦军. 基于未确知集合的故障诊断方法. 自动化学报, 2004, 30(5): 747-756)
[5]	Wu Qing-E. The Treatment Theory, Method and Application of Uncertain Information. Beijing: Science Press, 2009 (吴青娥. 不确定信息处理理论、方法及其应用. 北京: 科学出版社, 2009)
[6]	Li Ming, Wang Yan, Nian Fu-Zhong. Intelligent Information Processing and Application. Beijing: Electronic Industry Press, 2010 (李明, 王燕, 年福忠. 智能信息处理与应用. 北京: 电子工业出版社, 2010)
[7]	Vapnik V. N. The Nature of Statistical Learning Theory. New York: Springer, 1995
[8]	Deng Nai-Yang, Tian Ying-Jie. Theory, Algorithm and Extension of Support Vector Machine. Beijing: Science Press, 2009 (邓乃扬, 田英杰. 支持向量机——理论、算法与拓展. 北京: 科学出版社, 2009)
[9]	Zhang Xue-Gong. Introduction to statistical learning theory and support vector machines. Acta Automatica Sinica, 2000, 26(1): 32-42(张学工. 关于统计学习理论与支持向量机. 自动化学报, 2000, 26(1): 32-42)
[10]	Lin C F, Wang S D. Fuzzy support vector machines. IEEE Transactions on Neural Networks, 2002, 13(2): 464-471
[11]	Tao Q, Wang J. A new fuzzy support vector machine based on the weighted margin. Neural Procession Letters, 2004, 20(3): 139-150
[12]	Ji A B, Pang J H, Qiu H J. Support vector machine for classification based on fuzzy training data. Expert Systems with Applications, 2010, 37(4): 3495-3498
[13]	Yang Zhi-Min, Deng Nai-Yang. Fuzzy support vector classification based on possibility theory. Pattern Recognition and Artificial Intelligence, 2007, 20(1): 7-14(杨志民, 邓乃扬. 基于可能性理论的模糊支持向量分类机. 模式识别与人工智能, 2007, 20(1): 7-14)
[14]	Yang Z M, Yang X, Liu G L. A fuzzy optimization method for data mining. Journal of Convergence Information Technology, 2010, 5(5): 86-91
[15]	Zadeh L A. Fuzzy sets. Information and Control, 1965, 8(3): 338-353
[16]	Zadeh L A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1978, 1(1): 3-28
[17]	Peng Zu-Zeng, Sun Wen-Yu. Fuzzy Mathematics and Its Applications. Wuhan: Wuhan University Press, 2007 (彭祖赠, 孙韫玉. 模糊数学及其应用. 武汉: 武汉大学出版社, 2007)
[18]	Xie Ji-Jian, Liu Cheng-Ping. The Method and Applications of Fuzzy Mathematics. Wuhan: Huazhong University of Science and Technology Press, 2006 (谢季坚, 刘承平. 模糊数学方法及其应用. 武汉: 华中科技大学出版社, 2006)
[19]	Yang Zhi-Min, Deng Nai-Yang. Unascertained chance constrained programming. Systems Engineering, 2004, 22(4): 11-14(杨志民, 邓乃扬. 未确知机会约束规划. 系统工程, 2004, 22(4): 11-14)
[20]	Yang Zhi-Min, Liu Guang-Li. The Method and Applications of Uncertain Support Vector Machine. Beijing: Science Press, 2012 (杨志民, 刘广利. 不确定性支持向量机-算法及应用. 北京: 科学出版社, 2012)
[21]	Shivaswamy P K, Bhattacharyya C, Smola A J. Second order cone programming approaches for handling missing and uncertain data. Journal of Machine Learning Research, 2006, 7: 1283-1314
[22]	Li Xiao-Qing, Zhou Chang-Yin, Wang Yan-Chao. The method of unascertained chance constrained programming under the conditions of linear interdependence. Journal of Tangshan College, 2010, 23(6): 10-12(李小青, 周长银, 王延朝. 线性相依条件下未确知机会约束规划的解法. 唐山师范学院学报, 2010, 23(6): 10-12)
[23]	Yang Xu-Bing, Pan Zhi-Song, Chen Song-Can. Semi-supervised proximal support vector machine via generalized eigenvalues. Pattern Recognition and Artificial Intelligence, 2009, 22(3): 349-353(杨绪兵, 潘志松, 陈松灿. 半监督型广义特征值最接近支持向量机. 模式识别与人工智能, 2009, 22(3): 349-353)
[24]	Bennett K P, Demiriz A. Semi-supervised support vector machines. In: Advances in Neural Information Processing Systems. 1999, 11: 368-374
[25]	Yang Feng-Xia. Recognition of sub-health based on support vector machine. Modern Electronics Technique, 2009, 30(20): 167-170(杨凤霞. 基于支持向量机的亚健康状态识别. 现代电子技术, 2009, 30(20): 167-170)
[26]	Yuan Hui. The Characteristics Information Analysis of the Pulse Wave and the Study of Arteriosclerosis Diagnostic [Master dissertation], Shandong University, China, 2005(元慧. 脉搏波的特征信息分析和动脉硬化诊断研究 [硕士学位论文], 山东大学, 中国, 2005