ɛ-insensitive loss function is often employed in the twin support vector regression (TSVR). However, it can not effectively address the data with Gaussian noise. Huber loss function can suppress a variety of noise and outliers and yields great generalization performance. Motivated by this, we propose a novel twin support vector regression with Huber loss for the noise data in this paper. Experiments on nine benchmark datasets with different Gaussian noise show the validity of our proposed algorithm. Finally, we apply our method to the financial time series data that usually contain noise and outlier, and it also produces great performance.
VapnikV., The nature of statistical learning theory, Springer, New York, 1995.
2.
SchölkopfB., SmolaA.J., WilliamsonR.C. and BartlettP.L., New support vector algorithms, Neural Computation12 (2000), 1207–1245.
3.
Philip ChenC.L.,
WenG.,
LiuY. and WangF., Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks, IEEE Transactions on Neural Networks and Learning Systems25(6) (2014), 1217–1226.
4.
LiuY., TangL., TongS. and PhilipC.L., Chen, Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems, IEEE Transactions on Neural Networks and Learning Systems25(6) (2015), 1007–1018.
5.
LiuY., TongS., Philip ChenC.L. and
LiD., Neural controller design-based adaptive control for nonlinear MIMO systems with unknown hysteresis inputs, IEEE Transactions on Cybernetics46(1) (2016), 9–19.
6.
Philip ChenC.L.,
LiuY. and WenG., Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems, IEEE Transactions on Cybernetics44(5) (2014), 583–593.
7.
WenG., Philip ChenC.L.,
LiuY. and LiuZ., Neural-network based adaptive leader-following consensus control for second order non-linear multi-agent systems, IET Control Theory & Applications9(13) (2015), 1927–1934.
8.
LiuY., LiJ., TongS. and Philip ChenC.L., Neural network control-based adaptive learning design for nonlinear systems with full-state constraints, IEEE Transactions on Neural Networks and Learning Systems27(7) (2016), 1562–1571.
9.
LiS., WuH. and WanD., An effective feature selection method for hyperspectral image classification based on genetic algorithm and support vector machine, Knowledge-Based Systems24(1) (2011), 40–48.
10.
ZhangW., YoshidaT. and TangX., Text classification based on multi-word with support vector machine, Knowledge-Based Systems21(8) (2008), 879–886.
11.
LinF., YehC. and LeeM., The use of hybrid manifold learning and support vector machines in the prediction of business failure, Knowledge-Based Systems24(1) (2011), 95–101.
12.
Jayadeva,
KhemchandaniR. and ChandraS., Twin support vector machines for pattern classification, IEEE Transactions on Pattern Analysis and Machine Intelligence29(5) (2007), 905–910.
13.
FungG. and MangasarianO., Proximal support vector machine classifiers, In Seven International Proceedings on Knowledge Discovery and Data Mining, 2001, pp. 77–86.
14.
FungG. and MangasarianO., Multicategory proximal support vector machine classifiers, Machine Learning59 (2005), 77–97.
15.
GhoraiS., MukherjeeA. and DuttaP., Nonparallel plane proximal classifier, Signal Processing89(4) (2009), 510–522.
16.
PengX., A ν twin support vector machine for regression, Neural Networks23(3) (2010), 365–372.
17.
KumarM. and GopalM., Least squares twin support vector machines for pattern classification, Expert Systems with Applications36(4) (2009), 7535–7543.
18.
PengX., TSVR: An efficient twin support vector machine for regression, Neural Networks23(3) (2009), 365–372.
19.
CortesC. and VapnikV., Support vector networks, Machine Learning20(3) (1995), 273–297.
20.
VapnikV., GolowichS.E. and SmolaA., Support vector method for function approximation, regression estimation, and signal processing, In Advances in neural information processings system, 9, 1996, pp. 281–287.
21.
WuQ., A hybrid-forecasting model based on Gaussian support vector machine and chaotic particle swarm optimaization, Expert Systems with Applications37 (2009), 2388–2394.
22.
WuQ. and LawR., The forecasting model based on modified SVRM and PSO penalizing Gaussian noise, Expert Systems with Applications38(3) (2011), 1887–1894.
23.
WuQ. and YanH., Product sales forecasting model based on robust ν-support vector machine, Computer Integrated Manufacturing Systems15(6) (2009), 1081–1087.
24.
MehrkanoonS., HuangX. and SuykensJ.A.K., Non-parallel support vector classifiers with different loss functions, Neurocomputing143 (2014), 294–301.
25.
WangK. and ZhongP., Robust support vector regression with flexible loss function, International Journal of Signal Processing, Image Processing and Pattern Recognition7(4) (2014), 211–220.
26.
WangK., ZhuW. and ZhongP., Robust support vector regression with generalized loss function and applications, Neural Process Lett41 (2015), 89–106.
27.
HuQ., ZhangS., XieZ., MiJ. and WanJ., Noise model based ν-support vector regression with its application to short-term wind speed forecasting, Neural Networks57 (2014), 1–11.
28.
SuykensJ.A.K., LukasL. and VandewalleJ., Sparse approximation using least square vector machines, In IEEE International Symposium on Circuits and Systems, Geneva, Switzerland, 2000, pp. 757–760.
29.
HuberP.J., Robust estimation of a location parameter, The Annals of Mathematical Satistics35(1) (1964), 73–101.
30.
HuberP.J., Robust statistics, New York: Wiley, 1981.
31.
OlviL.M. and DavidR.M., Robust linear and support vector regression, IEEE Transactions on Pattern Analysis and Machine Intelligence22(9) (2000), 950–955.
32.
XuY. and WangL., A weighted twin support vector regression, Knowledge-Based Systems33 (2012), 92–101.
33.
XuY. and WangL., k-nearest neighbor-based weighted twin support vector regression, Applied Intelligence41(1) (2014), 299–309.
34.
ZhangJ. and WangY., A rough margin based support vector machine, Information Sciences178(9) (2008), 2204–2214.
