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Experimental Results ELM Weighted ELM Locally Weighted ELM Problem
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All training data are randomly chosen Targets are normalize -1 to 1 Features are normalize 0 to 1 Using RMSE criterion
K
yy
RMSE
K
i
ii
1
2)ˆ(
3
Sinc function: X=-10:0.05:10 Train:351 Test:50 (hidden neuron, h, k) Original
ELM(10)
Weighted ELM
(10,0.01)
Locally Weighted
ELM(10,1,20)
1.95E-1 9.41E-5 1.53E-4
x
x
)sin(
4
5
Function: X=-5:0.05:5 Train:151 Test:50 (hidden neuron, h, k)
6
2/2 2)21(1.1 xexxy
Original ELM(10)
Weighted ELM
(10,0.01)
Locally Weighted ELM
(10,1,20)
T2FNN
2.81E-1 1.39E-4 8.15E-4 1.3E-3
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Function: X1,x2,x3=-1:0.005:1 Train:351 Test:50 (hidden neuron, h, k)
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Original ELM(10)
Weighted ELM
(10,0.01)
Locally Weighted
ELM(10,1,20)
1.41E-4 3.09E-6 2.61E-5
)1( 23
31
22 xexy x
Machine CPU Feature:6 Train:100 Test:109 (hidden neuron, h, k)
Original ELM(10)
Weighted ELM
(10,0.9)
Locally Weighted
ELM(10,1,40)
0.111342 0.103473 0.105663
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Auto Price Feature:15 ,1 nominal ,14 continuous Train:80 Test:79 (hidden neuron, h, k)
Original ELM(15)
Weighted ELM
(10,0.9)
Locally Weighted
ELM(10,0.9,50)
0.201255 0.189584 0.193568
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Cancer Feature:32 Train:100 Test:94 (hidden neuron, h, k)
Original ELM(10)
Weighted ELM
(3,0.9)
Locally Weighted
ELM(3,1,40)
0.533656 0.528415 0.532317
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Input layer
hidden layer
output layer target, :
matrixght output wei the,:
matrixoutput layer hidden ,:
min
)()(
)()(
1
11
1111
mN
mj
jN
bgbg
bgbg
TT
jNjN
jj
T
β
H
THH)(Hβ
THβ
xwxw
xwxw
H
THβ
β
The weights between input layer and hidden layer and the biases of neurons in the hidden layer are randomly chosen.
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]1,0[bias,]1,1[weight
matrixdiagonal,
0
0
))/(5.0exp(
data testinga the:a
data trainingn the:n
feature ofnumber the:
~1,)(
11
2
th
th
1
2,,
NN
nnn
p
i
inian
w
w
hdw
p
Nnxxd
W
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WTWHWH)WH(β
WTWHβ
WTWHββ
TT )()(
min
1
14
Ex
3648.0
2778.0
002.0
2365.0
5505.1)(
9.0
7.0
5.0
4013.0
4502.0
4750.0
]4.0;2.0;1.0[
1
THβ
THHHβ
TH
X
TT
15
3628.0
2759.0
0007.0
2355.0
5534.1)())((
9975.000
09975.00
0099.0
]1.0;1.0;2.0[
1targettesting,0.3
1
WTWHβ
TWHWHWHβ
W
d
TT
為為假設
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Find the k nearest training data to testing data
WTWHWH)WH(β
WTWHβ
W
TT
kkw
w
)()(
matrixdiagonal,
0
0
1
11
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Paper數據 Randomly weight and bias The output of Nearest data (feature selection…?)
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-0.9318
2
0.312205
0.029309
0.061562
0 0 0
1-
0.95352
0.25826
0.060621
0.061562
00.0192
310.0056
82
2-
0.98056
0.393122
0.022044
0.03028
00.0192
310.0056
82
3-
0.97946
0.211059
0.029309
0.045921
00.0384
620.0227
27
6 -0.94930.2043
160.0060
120.0928
430
0.019231
0.034091
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