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Neural Processing Letters

Erschienen in:

05.09.2017

Stochastic Support Vector Machine for Classifying and Regression of Random Variables

verfasst von: Maryam Abaszade, Sohrab Effati

Erschienen in: Neural Processing Letters | Ausgabe 1/2018

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Abstract

Support vector machine (SVM) is a supervised machine learning method which can be used for both classification and regression models. In this paper, we introduce a new model of SVM and support vector regression which any of training samples containing inputs and outputs are considered the random variables with known or unknown probability functions. In this new models, we need the mathematical expectation for any of training samples but when these are unknown we apply nonparametric statistical methods. Also constraints occurrence have probability function which helps obtain maximum margin and achieve robustness. We obtain the optimal separating hyperplane and the optimal hyperplane regression by solving the quadratic optimization problems. Finally the proposed methods are illustrated by several experiments.

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Vapnik V (1998) The nature of statistical learning theory. Springer-Verlag, New YorkMATH

Drucker H, Burges CJC, Kaufman L, Smola A, Vapnik V (1997) Support vector regression machines. Adv Neural Inf Process Syst 9:155–161

Suykens J, VanGestel T, DeBrabanter J, DeMoor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, SingaporeCrossRef

Li H, Yang J, Zhang G, Fan B (2013) Probabilistic support vector machines for classification of noise affected data. Inf Sci 221:60–71CrossRef

Gao JB, Gunn SR, Harris CJ, Brown M (2002) A probabilistic framework for SVM regression and error bar estimation. Mach Learn 46:71–89CrossRefMATH

Jinglin Y, Li HX, Yong H (2011) A probabilistic SVM based decision system for pain diagnosis. Expert Syst Appl 38:9346–9351CrossRef

Trafalis TB, Gilbert RC (2006) Robust classification and regression using support vector machines. Eur J Oper Res 173:893–909MathSciNetCrossRefMATH

Ben-Tal A, Bhadra S, Bhattacharyya Ch, Nath JS (2011) Chance constrained uncertain classification via robust optimization. Math Progr 127:145–173MathSciNetCrossRefMATH

Trafalis TB, Alwazzi SA (2007) Support vector regression with noisy data: a second order cone programming approach. Int J Gen Syst 36:237–250MathSciNetCrossRefMATH

10.

Lobo M, Vandenberghe L, Boyd S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra Appl 284:193–228MathSciNetCrossRefMATH

11.

Mehrotra S (1992) On the implementation of a primal-dual interior point method. SIAM J Opt 2:575–601MathSciNetCrossRefMATH

12.

Shivaswamy PK, Bhattacharyya Ch, Smola AJ (2006) Second order cone programming approaches for handling missing and uncertain data. J Mach Learn Res 7:1283–1314MathSciNetMATH

13.

Carrizosa E, Gordillo JE, Plastria F (2008) Kernel support vector regression with imprecise output. MOSI, Vrije Univ Brussel, Brussel, Belgium, Technical Report, Dept

14.

Park WJ, Kil RM (2009) Pattern classification with class probability output network. IEEE Trans Neural Netw 20:1659–1673CrossRef

15.

Kim S, Yua Z, Kil RM, Lee M (2014) Deep learning of support vector machines with class probability output networks. Neural Netw 64:19–28CrossRef

16.

Thi HAL, Vo XT, Dinh TP (2014) Feature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions algorithms. Neural Netw 59:36–50CrossRefMATH

17.

Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501CrossRef

18.

Sun Y, Yuan Y, Wang G (2014) Extreme learning machine for classification over uncertain data. Neurocomputing 128:500–506CrossRef

19.

Sadoghi Yazdi H, Effati S, Saberi Z (2007) The probabilistic constraints in the support vector machine. Appl Math Comput 194:467–479MathSciNetMATH

20.

Lanckriet GRG, Ghaoui LE, Bhattacharyya Ch, Jordan MI (2002) A robust minimax approach to classification. J Mach Learn Res 3:555–582MathSciNetMATH

21.

Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20:273–297MATH

22.

Barnett NS, Dragomir SS (2002) Some inequalities for probability, expectation and variance of random variables defined over a finite interval. Comput Math Appl 43:1319–1357MathSciNetCrossRefMATH

23.

Karr AF (1992) Probability. Springer, New YorkMATH

24.

http://www.wisostat.uni-koeln.de/28969.html?&L=1

25.

Bache K, Lichman M (2013) UCI machine learning repository. http://archive.ics.uci.edu/ml/machine-learning-databases/

26.

Hastie TJ, Tibshirani RJ (1990) Generalized additive models. CRC Press. http://www.dcc.fc.up.pt/~ltorgo/Regression/DataSets.html

27.

Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1–26MathSciNetCrossRefMATH

Titel: Stochastic Support Vector Machine for Classifying and Regression of Random Variables
verfasst von: Maryam Abaszade
Sohrab Effati
Publikationsdatum: 05.09.2017
Verlag: Springer US
Erschienen in: Neural Processing Letters / Ausgabe 1/2018
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-017-9697-0

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