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Microsoft Word - 17-p2097-171154.doc 48 8 () Vol.48 No.8 20178
Journal of Central South University (Science and Technology) Aug.
2017
DOI: 10.11817/j.issn.1672−7207.2017.08.017
FLS-SVM
1, 2 2
(1. 410083 2 410205)
(fuzzy least squares support vector machine, FLS-SVM) FLS-SVM
(improved fuzzy least squares support vector machines, IFLS-SVM) Ripley MONK
PIMA
LS-SVM FLS-SVM IFLS-SVM
TP183 A 1672−7207(2017)08−2097−08
An improved FLS-SVM classification identification model and its application
ZUO Hongyan1, 2, WANG Taosheng2
(1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China;
2. School of Business, Hunan International Economics University, Changsha 410205, China)
Abstract: A classification and identification model was developed based on improved fuzzy least squares support vector machines(FLS-SVM),in which the fuzzy membership function was set by using triangle function method and its parameters were optimized by an adaptive mutative scale chaos immune algorithm, and an improved fuzzy least squares support vector machines(IFLS-SVM) was constructed. The simulation experiments were conducted on three benchmarking datasets such as Ripley datasets, MONK datasets and PIMA datasets for testing the generalization performance of the classification and identification model, signals from underground metal mines stope wall rock and international trade data in China were diagnosed by the IFLS-SVM classification and identification model. The results show that compared with LS-SVM classification identification model and FLS-SVM classification identification model, the IFLS-SVM classification identification model is valid for improving the analysis accuracy of the data with noises or outliers and IFLS-SVM classification identification model has small relative error. Key words: chaos immune algorithm; fuzzy support vector machines; classification identification
(support vector machineSVM)[1−3]
2016−12−182017−02−21 (Foundation item)(71573082)(2017JJ2134)
(14K055)(Project(71573082) supported by the National Natural Science Foundation of China; Project(2017JJ2134) supported by the Natural Science Foundation of Hunan Province; Project(14K055) supported by the Innovation Platform Open Fund of Hunan Province)
()[email protected]
() 48
(fuzzy least squares support vector machine, FLS-SVM)[10−11]
FLS-SVM
(improved fuzzy least squares support vector machines, IFLS-SVM)
(xl, yl, μ(xl))k=12…l
xkykμ(xk)
(1) [15]
CJ xξ μ ε =
= ⋅ + ⋅∑w w w (1)
s.t. yi= wTφ(xi)+b+εk εk0k=12…l εkC b
T
1 [ ( ) ]
l
L J a x b yε =
= − ⋅ + + −∑ w (2)
1
(3)
y=[y1…yk…yl]TE=[1…1…1 l]Ta=[a1…ak…al]Tij=φ(xk)φ(xt)=K(xk, xt) t=12…l
FLS-SVM 1
1 ( ) ( , )
l
= +∑y x K x (4)
x=[x1…xk…xl]K(xk, x)=exp{-|xk-x|2/σ2} σ
1 FLS-SVM
1.2 FLS-SVM
2
i
z u m m
(5)
zij i j ui i mi i
i
2099
2 2 2( ) ( ) ( )ij i ij i ij i i
z z z T
μ μ μ σ
1.3 FLS-SVM
FLS-SVM
FLS-SVM
2
1
1( , ) [ ( ) ]
n
σ
10−3 EMS FLS-SVM
−∑[ (8)
f(xi)yi FLS-SVM
Step 1 x=[x1…xk…xl]{Ag}
sn+1=4sn(1−sn)
N
{Ab} Step 2 Agi Step 2.1 (9) Abiz
Agjz βij
A Aβ =
Nc Step 2.3 z
Cij(z+1)=Cijz−α(Cijz−Xijz)(Cijz z Xijz z α )
Step 2.4 z
Cij(z+1) z−1 Cijz
C Cγ + =
Mp Step 2.6 (11) Abi Abj
λij Mp λij
σs
A Aλ =
M Step 4 15%
X=(X1…Xt…XT)
( ) ( )
′ = + −
φ∈(0, 0.4)
ta′at ta′=at tb′bt
tb′ =btXt[ ta′ tb′ ]
Yt
Yt Xt
(1 ) + (1 )t t t t t t t t tδ δ δ δ′ = − + −X Y X Y X (14)
δt0δt1
δt 3ln 11
Step 5 sn+1=4sn(1−sn) N ′(0, 1)
*) f(Xt
* Step 7 EMS10−5
X Step 1 1.4 IFLS-SVM
IFLS-SVM
1) Ripley 2 Ripley
300 ( 150 )
1 000 ( 500 ) 2) MONK
3 MONK 130 (
65 65 ) 440 (
230 210 ) 3) PIMAPIMA 800(
500 300 )
600 200 3 (UCI)
LS-SVM FLS-SVM IFLS-SVM
3
1
1
LS-SVM
analysis accuracy is optimal
σ 1.10 1.2 0.65
σ 1.00 0.8 0.76
σ 2.00 3.0 4.50
CPU IFLS-SVM
CPU
Table 3 Comparison of consuming time of three kinds of
classification models s
600
150 75 (
25 25 25 )75 ( 25
25 25 ) LS-SVM FLS-SVM IFLS-SVM
4
4 LS-SVM FLS-SVM IFLS-SVM
82.67%86.67% 90.67% IFLS-SVM
2101
3
4
IFLS-SVM
5 IFLS-SVM
5 A ()R1=(l 0000)B () R2=(01000) C ()R3=(00l00)D () R4=(000l0)E ()R5=(0000 1)IFLS-SVM
Ri(i=12345) 2.2.3
1980—2014
2007—2014
5 IFLS-SVM ( F2 )
5[10] ( F1 )
(5)(6) 5
Ri(i=12…5) IFLS-SVM
1980—2006 x1x2x3
x4x5 x6
IFLS-SVM
6 6 F2
0.70% Ri(i=12…5)
IFLS-SVM 2007—2014 x1x2x3x4x5 x6 IFLS-SVM
0.90% IFLS-SVM IFLS-SVM
γi
5 xi
Table 5 Capability index parameters xi(i=1, 2, …, 5) for international trade safety in China
x1/ x2/ x3/ x4/ x5/1 x6/ Ri
1980 2 983.00 15.00 399.50 −13.00 1.498 4 300.41 R5
1981 961.00 25.00 523.70 27.10 1.705.0 415.03 R5
…
…
…
…
…
…
…
…
2005 88 773.60 638.05 1 41051.00 8 188.72 8.191 7 24 015.41 R3
2006 109 998.20 735.72 161 587.30 10 663.40 7.971 8 29 310.37 R3
2007 13 732.94 826.58 172 534.20 15 282.50 7.604 0 27 949.13 R3
2008 172 828.40 923.95 217 885.40 19 460.30 6.945 1 36 673.15 R2
2009 224 598.77 900.30 260 772.00 23 991.50 6.831 0 41 082.37 R1
2010 27 812.85 1 100.00 303 302.50 28 473.40 6.769 5 40 758.58 R2
2011 311 485.13 1 150.50 34 363 509.00 31 811.50 6.458 8 41 600.00 R3
2012 364 835.00 1 117.20 399 551.00 33 116.00 6.312 5 974 159.50 R2
2013 447 074.00 1 175.86 447 602.00 38 213.00 6.192 3 1 106 500.00 R2
2014 502 005.00 1 195.60 503 000.00 38 430.00 6.216 6 1 228 400.00 R2
6 IFLS-SVM
Table 6 Training results of IFLS-SVM classification and identification model based on China international trade safety
×100 /%
F1 F2 F1 F2
…
…
…
…
…
…
2005 R3(0, 0, 1, 0, 0) (0.59, 0.76, 98.45, 0.75, 0.61)) (0.22, 0.28, 99.39,0.31, 0.23) 1.55 0.61
2006 R3(0, 0, 1, 0, 0) (0.78, 0.64, 98.42, 0.77, 0.95) (0.21, 0.22, 99.48, 0.17, 0.23) 1.58 0.52
7 IFLS-SVM
Table 7 Test results of IFLS-SVM classification and identification model after training
×100 /%
F1 F2 F1 F2
2007 R3(0, 0, 1, 0, 0) (0.48, 0.56, 98.45, 0.45, 0.62) (0.17, 0.18, 99.25, 0.18, 0.22) 1.35 0.75
2008 R2(0, 1, 0, 0, 0) (0.91, 98.67, 0.83, 0.54, 0.63) (0.18, 99.34, 0.18, 0.26, 0.23) 1.33 0.66
2009 R1(1, 0, 0, 0, 0) (98.56, 0.86, 0.89, 1.12, 0.98) (99.37, 0.21, 0.22, 0.28, 0.25) 1.44 0.63
2010 R2(0, 1, 0, 0, 0) (0.72, 98.55, 0.73, 0.64, 0.49) (0.19, 99.63, 0.18, 0.16, 0.23) 1.45 0.47
2011 R3(0, 0, 1, 0, 0) (0.89, 0.88, 98.48, 0.86, 0.86) (0.12, 0.10, 99.31, 0.17, 0.12) 1.52 0.69
2012 R3(0, 0, 1, 0, 0) (0.58, 0.76, 98.38, 0.45, 0.62) (0.17, 0.18, 99.22, 0.18, 0.22) 1.52 0.78
2013 R1(1, 0, 0, 0, 0) (98.23, 0.86, 0.89, 1.12, 0.98) (99.25, 0.21, 0.22, 0.28, 0.25) 1.77 0.75
2014 R2(0, 1, 0, 0, 0) (0.91, 98.12, 0.83, 0.54, 0.63) (0.18, 99.15, 0.18, 0.26, 0.23) 1.88 0.85
4 4
γ1 γ6
γ5 γ2
2103
IFLS-SVM
about international trade safety in China
3
IFLS-SVM
x1 x6
x5 x2 x4
x3 [1] MONTEIRO R V A, GUIMARÃES G C, MOURA F A M, et al.
Estimating photovoltaic power generation: performance analysis
of artificial neural networks, support vector machine and Kalman
filter[J]. Electric Power Systems Research, 2017, 143: 643−656.
[2] COUELLAN N, WANG Wenjuan. Uncertainty-safe large scale
support vector machines[J]. Computational Statistics & Data
Analysis, 2017, 109: 215−230.
[3] ABD A M, ABD S M. Modelling the strength of lightweight
foamed concrete using support vector machine(SVM)[J]. Case
Studies in Construction Materials, 2017, 6: 8−15.
[4] LIU Chuan, WANG Wenyong, WANG Meng, et al. An efficient
instance selection algorithm to reconstruct training set for
support vector machine[J]. Knowledge-Based Systems, 2017,
116: 58−73.
recognition of moving target based on empirical mode
decomposition and genetic algorithm support vector[J]. Journal
of Central South University, 2015, 22(4): 1389−1396.
[6] CARRIZOSA E, NOGALES-GÓMEZ A, MORALES D R.
Clustering categories in support vector machines[J]. Omega,
2017, 66(Part A): 28−37.
[7] WANG Di, ZHANG Xiaoqin, FAN Mingyu, et al. Hierarchical
mixing linear support vector machines for nonlinear
classification[J]. Pattern Recognition, 2016, 59: 255−267.
[8] HANG Jun, ZHANG Jianzhong, CHENG Ming. Application of
multi-class fuzzy support vector machine classifier for fault
diagnosis of wind turbine[J]. Fuzzy Sets and Systems, 2016, 297:
128−140.
classification[J]. Pattern Recognition,2015, 48(6): 2110−2117.
[10] ÇOMAK E, POLAT K, GÜNE S, et al. A new medical
decision making system: Least square support vector machine
(LSSVM) with fuzzy weighting pre-processing[J]. Expert
Systems with Applications, 2007, 32(2): 409−414
[11] WANG Chunpeng, WANG Xingyuan, ZHANG Chuan, et al.
Geometric correction based color image watermarking using
fuzzy least squares support vector machine and Bessel K form
distribution[J]. Signal Processing, 2017, 134: 197−208.
[12] , , , .
[J]. (), 2013, 44(1):
202−207.
WANG Zhiqiang, LI Lijun, HUANG Yan, et al. Fire disaster
signal recognition based on fuzzy least squares support vector
machines[J]. Journal of Central South University (Science
and Technology), 2013, 44(1): 202−207.
() 48
[J]. (), 2014, 52(2):
313−318.
vector machine[J]. Journal of Jilin University (Science Edition),
2014, 52(2): 313−318.
[14] ZUO Hongyan, LUO Zhouquan, GUAN Jialin, et al.
Identification on rock and soil parameters for vibration drilling
rock in metal mine based on fuzzy least square support vector
machine[J]. Journal of Central South University, 2014, 21(3):
1085−1090.
vector machines soft measurement model based on adaptive
mutative scale chaos immune algorithm[J]. Journal of Central
South University, 2014, 21(2): 593−599.
[16] VAPNIK V. Statistical learning theory[M]. New York: Wiley,
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[18] . T-S [J].
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169−174.
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electromechanical products and its risk prediction[M]. Changsha:
Central South University Press, 2015: 140−141.
( )
DOI: 10.11817/j.issn.1672−7207.2017.08.017
FLS-SVM
1, 2 2
(1. 410083 2 410205)
(fuzzy least squares support vector machine, FLS-SVM) FLS-SVM
(improved fuzzy least squares support vector machines, IFLS-SVM) Ripley MONK
PIMA
LS-SVM FLS-SVM IFLS-SVM
TP183 A 1672−7207(2017)08−2097−08
An improved FLS-SVM classification identification model and its application
ZUO Hongyan1, 2, WANG Taosheng2
(1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China;
2. School of Business, Hunan International Economics University, Changsha 410205, China)
Abstract: A classification and identification model was developed based on improved fuzzy least squares support vector machines(FLS-SVM),in which the fuzzy membership function was set by using triangle function method and its parameters were optimized by an adaptive mutative scale chaos immune algorithm, and an improved fuzzy least squares support vector machines(IFLS-SVM) was constructed. The simulation experiments were conducted on three benchmarking datasets such as Ripley datasets, MONK datasets and PIMA datasets for testing the generalization performance of the classification and identification model, signals from underground metal mines stope wall rock and international trade data in China were diagnosed by the IFLS-SVM classification and identification model. The results show that compared with LS-SVM classification identification model and FLS-SVM classification identification model, the IFLS-SVM classification identification model is valid for improving the analysis accuracy of the data with noises or outliers and IFLS-SVM classification identification model has small relative error. Key words: chaos immune algorithm; fuzzy support vector machines; classification identification
(support vector machineSVM)[1−3]
2016−12−182017−02−21 (Foundation item)(71573082)(2017JJ2134)
(14K055)(Project(71573082) supported by the National Natural Science Foundation of China; Project(2017JJ2134) supported by the Natural Science Foundation of Hunan Province; Project(14K055) supported by the Innovation Platform Open Fund of Hunan Province)
()[email protected]
() 48
(fuzzy least squares support vector machine, FLS-SVM)[10−11]
FLS-SVM
(improved fuzzy least squares support vector machines, IFLS-SVM)
(xl, yl, μ(xl))k=12…l
xkykμ(xk)
(1) [15]
CJ xξ μ ε =
= ⋅ + ⋅∑w w w (1)
s.t. yi= wTφ(xi)+b+εk εk0k=12…l εkC b
T
1 [ ( ) ]
l
L J a x b yε =
= − ⋅ + + −∑ w (2)
1
(3)
y=[y1…yk…yl]TE=[1…1…1 l]Ta=[a1…ak…al]Tij=φ(xk)φ(xt)=K(xk, xt) t=12…l
FLS-SVM 1
1 ( ) ( , )
l
= +∑y x K x (4)
x=[x1…xk…xl]K(xk, x)=exp{-|xk-x|2/σ2} σ
1 FLS-SVM
1.2 FLS-SVM
2
i
z u m m
(5)
zij i j ui i mi i
i
2099
2 2 2( ) ( ) ( )ij i ij i ij i i
z z z T
μ μ μ σ
1.3 FLS-SVM
FLS-SVM
FLS-SVM
2
1
1( , ) [ ( ) ]
n
σ
10−3 EMS FLS-SVM
−∑[ (8)
f(xi)yi FLS-SVM
Step 1 x=[x1…xk…xl]{Ag}
sn+1=4sn(1−sn)
N
{Ab} Step 2 Agi Step 2.1 (9) Abiz
Agjz βij
A Aβ =
Nc Step 2.3 z
Cij(z+1)=Cijz−α(Cijz−Xijz)(Cijz z Xijz z α )
Step 2.4 z
Cij(z+1) z−1 Cijz
C Cγ + =
Mp Step 2.6 (11) Abi Abj
λij Mp λij
σs
A Aλ =
M Step 4 15%
X=(X1…Xt…XT)
( ) ( )
′ = + −
φ∈(0, 0.4)
ta′at ta′=at tb′bt
tb′ =btXt[ ta′ tb′ ]
Yt
Yt Xt
(1 ) + (1 )t t t t t t t t tδ δ δ δ′ = − + −X Y X Y X (14)
δt0δt1
δt 3ln 11
Step 5 sn+1=4sn(1−sn) N ′(0, 1)
*) f(Xt
* Step 7 EMS10−5
X Step 1 1.4 IFLS-SVM
IFLS-SVM
1) Ripley 2 Ripley
300 ( 150 )
1 000 ( 500 ) 2) MONK
3 MONK 130 (
65 65 ) 440 (
230 210 ) 3) PIMAPIMA 800(
500 300 )
600 200 3 (UCI)
LS-SVM FLS-SVM IFLS-SVM
3
1
1
LS-SVM
analysis accuracy is optimal
σ 1.10 1.2 0.65
σ 1.00 0.8 0.76
σ 2.00 3.0 4.50
CPU IFLS-SVM
CPU
Table 3 Comparison of consuming time of three kinds of
classification models s
600
150 75 (
25 25 25 )75 ( 25
25 25 ) LS-SVM FLS-SVM IFLS-SVM
4
4 LS-SVM FLS-SVM IFLS-SVM
82.67%86.67% 90.67% IFLS-SVM
2101
3
4
IFLS-SVM
5 IFLS-SVM
5 A ()R1=(l 0000)B () R2=(01000) C ()R3=(00l00)D () R4=(000l0)E ()R5=(0000 1)IFLS-SVM
Ri(i=12345) 2.2.3
1980—2014
2007—2014
5 IFLS-SVM ( F2 )
5[10] ( F1 )
(5)(6) 5
Ri(i=12…5) IFLS-SVM
1980—2006 x1x2x3
x4x5 x6
IFLS-SVM
6 6 F2
0.70% Ri(i=12…5)
IFLS-SVM 2007—2014 x1x2x3x4x5 x6 IFLS-SVM
0.90% IFLS-SVM IFLS-SVM
γi
5 xi
Table 5 Capability index parameters xi(i=1, 2, …, 5) for international trade safety in China
x1/ x2/ x3/ x4/ x5/1 x6/ Ri
1980 2 983.00 15.00 399.50 −13.00 1.498 4 300.41 R5
1981 961.00 25.00 523.70 27.10 1.705.0 415.03 R5
…
…
…
…
…
…
…
…
2005 88 773.60 638.05 1 41051.00 8 188.72 8.191 7 24 015.41 R3
2006 109 998.20 735.72 161 587.30 10 663.40 7.971 8 29 310.37 R3
2007 13 732.94 826.58 172 534.20 15 282.50 7.604 0 27 949.13 R3
2008 172 828.40 923.95 217 885.40 19 460.30 6.945 1 36 673.15 R2
2009 224 598.77 900.30 260 772.00 23 991.50 6.831 0 41 082.37 R1
2010 27 812.85 1 100.00 303 302.50 28 473.40 6.769 5 40 758.58 R2
2011 311 485.13 1 150.50 34 363 509.00 31 811.50 6.458 8 41 600.00 R3
2012 364 835.00 1 117.20 399 551.00 33 116.00 6.312 5 974 159.50 R2
2013 447 074.00 1 175.86 447 602.00 38 213.00 6.192 3 1 106 500.00 R2
2014 502 005.00 1 195.60 503 000.00 38 430.00 6.216 6 1 228 400.00 R2
6 IFLS-SVM
Table 6 Training results of IFLS-SVM classification and identification model based on China international trade safety
×100 /%
F1 F2 F1 F2
…
…
…
…
…
…
2005 R3(0, 0, 1, 0, 0) (0.59, 0.76, 98.45, 0.75, 0.61)) (0.22, 0.28, 99.39,0.31, 0.23) 1.55 0.61
2006 R3(0, 0, 1, 0, 0) (0.78, 0.64, 98.42, 0.77, 0.95) (0.21, 0.22, 99.48, 0.17, 0.23) 1.58 0.52
7 IFLS-SVM
Table 7 Test results of IFLS-SVM classification and identification model after training
×100 /%
F1 F2 F1 F2
2007 R3(0, 0, 1, 0, 0) (0.48, 0.56, 98.45, 0.45, 0.62) (0.17, 0.18, 99.25, 0.18, 0.22) 1.35 0.75
2008 R2(0, 1, 0, 0, 0) (0.91, 98.67, 0.83, 0.54, 0.63) (0.18, 99.34, 0.18, 0.26, 0.23) 1.33 0.66
2009 R1(1, 0, 0, 0, 0) (98.56, 0.86, 0.89, 1.12, 0.98) (99.37, 0.21, 0.22, 0.28, 0.25) 1.44 0.63
2010 R2(0, 1, 0, 0, 0) (0.72, 98.55, 0.73, 0.64, 0.49) (0.19, 99.63, 0.18, 0.16, 0.23) 1.45 0.47
2011 R3(0, 0, 1, 0, 0) (0.89, 0.88, 98.48, 0.86, 0.86) (0.12, 0.10, 99.31, 0.17, 0.12) 1.52 0.69
2012 R3(0, 0, 1, 0, 0) (0.58, 0.76, 98.38, 0.45, 0.62) (0.17, 0.18, 99.22, 0.18, 0.22) 1.52 0.78
2013 R1(1, 0, 0, 0, 0) (98.23, 0.86, 0.89, 1.12, 0.98) (99.25, 0.21, 0.22, 0.28, 0.25) 1.77 0.75
2014 R2(0, 1, 0, 0, 0) (0.91, 98.12, 0.83, 0.54, 0.63) (0.18, 99.15, 0.18, 0.26, 0.23) 1.88 0.85
4 4
γ1 γ6
γ5 γ2
2103
IFLS-SVM
about international trade safety in China
3
IFLS-SVM
x1 x6
x5 x2 x4
x3 [1] MONTEIRO R V A, GUIMARÃES G C, MOURA F A M, et al.
Estimating photovoltaic power generation: performance analysis
of artificial neural networks, support vector machine and Kalman
filter[J]. Electric Power Systems Research, 2017, 143: 643−656.
[2] COUELLAN N, WANG Wenjuan. Uncertainty-safe large scale
support vector machines[J]. Computational Statistics & Data
Analysis, 2017, 109: 215−230.
[3] ABD A M, ABD S M. Modelling the strength of lightweight
foamed concrete using support vector machine(SVM)[J]. Case
Studies in Construction Materials, 2017, 6: 8−15.
[4] LIU Chuan, WANG Wenyong, WANG Meng, et al. An efficient
instance selection algorithm to reconstruct training set for
support vector machine[J]. Knowledge-Based Systems, 2017,
116: 58−73.
recognition of moving target based on empirical mode
decomposition and genetic algorithm support vector[J]. Journal
of Central South University, 2015, 22(4): 1389−1396.
[6] CARRIZOSA E, NOGALES-GÓMEZ A, MORALES D R.
Clustering categories in support vector machines[J]. Omega,
2017, 66(Part A): 28−37.
[7] WANG Di, ZHANG Xiaoqin, FAN Mingyu, et al. Hierarchical
mixing linear support vector machines for nonlinear
classification[J]. Pattern Recognition, 2016, 59: 255−267.
[8] HANG Jun, ZHANG Jianzhong, CHENG Ming. Application of
multi-class fuzzy support vector machine classifier for fault
diagnosis of wind turbine[J]. Fuzzy Sets and Systems, 2016, 297:
128−140.
classification[J]. Pattern Recognition,2015, 48(6): 2110−2117.
[10] ÇOMAK E, POLAT K, GÜNE S, et al. A new medical
decision making system: Least square support vector machine
(LSSVM) with fuzzy weighting pre-processing[J]. Expert
Systems with Applications, 2007, 32(2): 409−414
[11] WANG Chunpeng, WANG Xingyuan, ZHANG Chuan, et al.
Geometric correction based color image watermarking using
fuzzy least squares support vector machine and Bessel K form
distribution[J]. Signal Processing, 2017, 134: 197−208.
[12] , , , .
[J]. (), 2013, 44(1):
202−207.
WANG Zhiqiang, LI Lijun, HUANG Yan, et al. Fire disaster
signal recognition based on fuzzy least squares support vector
machines[J]. Journal of Central South University (Science
and Technology), 2013, 44(1): 202−207.
() 48
[J]. (), 2014, 52(2):
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