Download An Input Variable Selection Method for the Artificial Neural Network

An Input Variable Selection Method for the Artificial Neural Network of Shear
Stiffness of Worsted Fabrics
Ting Chen*, Chong Zhang, Xia Chen and Liqing Li
College of Textile and Clothing Engineering, Soochow University, Suzhou 215021, China
Received 9 January 2008; revised 12 August 2008; accepted 18 August 2008
DOI:10.1002/sam.10020
Published online in Wiley InterScience (www.interscience.wiley.com).
Abstract: The relationship between yarn properties, fabric parameters, and shear stiffness of worsted fabrics is modeled using
the soft computing technique. Because of the small number of samples, the artificial neural network model to be established
must be a small-scale one. Therefore, this soft computing approach includes two stages. First, the yarn properties and fabric
parameters are selected by utilizing an input variable selection method, so as to find the most relevant yarn properties and fabric
parameters as the input variables to fit the small-scale artificial neural network model. The first part of this method takes the
human knowledge on the shear stiffness of fabrics into account. The second part utilizes a data sensitivity criterion based on
a distance method. Second, the artificial neural network model of the relationship between yarn properties, fabric parameters,
and shear stiffness of fabrics is established. The results show that the artificial neural network model yields accurate prediction
and a reasonably good artificial neural network model can be achieved with relatively few data points by integrating with the
input variable selecting method developed in this research. The results also show that there is great potential for this research
in the field of computer-assisted design in textile technology.  2009 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 1:
000–000, 2009
Keywords:
modeling; soft computing; input variable selection; shear stiffness
1. INTRODUCTION
Shear stiffness is one of the important properties of
worsted fabrics. It is well known that the shear stiffness
depends on yarn properties and fabric parameters. Understanding the relationship between yarn properties, fabric
parameters, and shear stiffness is vital to optimize the selection of yarns and improve the fabric quality.
As a nonlinear problem, predicting the shear stiffness
can be realized by an alternative modeling method, that
is, by using the artificial neural network (ANN) model.
ANN models have been shown to provide good approximations in presence of noisy data and smaller number
of experimental points and the assumptions under which
ANN models work are less strict than those for statistical models [1]. Over the past decades, the ANNs have
been used for modeling various textile nonlinear problems
[2–8].
In recent years, some approaches have been developed
for selecting the relevant input variables in ANN modeling.
Thirumalaiah and Deo used a priori knowledge to select
the input variables [9]. Although it is easy to perform, it is
Correspondence to: Ting Chen ([email protected])
 2009 Wiley Periodicals, Inc.
dependent on an expert’s knowledge, and hence it is very
subjective and case dependent.
Cai et al. used the correlation analysis technique for
variable selection in ANN estimation of battery state of
charge [10]. The major disadvantage is that it is unable to
capture any nonlinear dependence that may exist between
the inputs and the output, and may possibly result in the
omission of important inputs that are related to the output
in a nonlinear fashion.
Drezga and Rahman put forward a phase-space embedding method for input variable selection for ANN-based
short-term load forecasting [11]. However, this method
can hardly deal with such associated variables as weather,
and the computing procedure is rather complicated. The
predicted results were dissatisfactory when incorporating
directly the selected inputs into the model unless other
variables such as time and weather are also incorporated.
Gao and Shan utilized the orthogonal least squares (OLS)
method to select input variables [12]. OLS method calculates the individual contribution of each input variable to
an output variable by performing orthogonal transformation
on each input variable. Its disadvantage is that it cannot be
applied to continuous time data series and also leads to
complex computation.
Statistical Analysis and Data Mining, Vol. (In press)
Utans et al. proposed a sensitivity-based pruning method
for input variable selection [13]. With this algorithm, candidate architectures are constructed by evaluating the effect
of removing an input variable from the fully connected network. These are ranked in order of increasing training error.
Inputs are then removed following a ‘Best First’ strategy,
that is, selecting the input that, when removed, increases the
training error least. The main disadvantage of this approach
is that it is based on trial and error, and as such, there is no
guarantee that they will find the globally best subsets, and
it is also computationally intensive.
Chen et al. applied principal component analysis (PCA)
to reduce the number of input nodes for ANNs for classification of wholesome and unwholesome poultry carcasses [14]. However, there are three disadvantages to
using PCA. First, PCA is a linear technique and nonlinear
relationships between the inputs are ignored while estimating each principal component. Second, the variables in
the principal component space do not have any physical
meaning and are difficult to interpret. Third, the principal
components are simply transformations of the input variables, determined without taking the output variable into
account. Hence, the first few principal components may
not necessarily be the most important for predicting the
output.
Nonlinear principal component analysis (NLPCA) is
a generalization of PCA as it can uncover and remove
nonlinear relationships between the input variables [15].
NLPCA operates by training a feed forward neural network to perform auto-association: the network outputs
are same as the network inputs. However, the nonlinear
principal components are even more complex and difficult to interpret than the linear principal components.
NLPCA is also a transformation of the input space and
does not account for the output, while determining each
nonlinear principal component. There is an additional difficulty associated with training an ANN to accomplish
NLPCA.
Abrahart et al. used the saliency analysis to disaggregate an ANN solution in terms of its forecasting inputs
[16]. In this approach, the effect that each input has on
the error function is examined by removing one input
at a time from the trained ANN model. The saliency
analysis was achieved by setting one input data stream
at a time to zero, performing the forecasting using the
trained ANN, replacing the input data stream after the
computation and repeating the process on the next input,
and so on. In this way, the relative importance of each
input was determined by examining the change in forecasting error. However, the main disadvantage of this
approach is that they did not retain the ANN removing
each input.
Statistical Analysis and Data Mining DOI:10.1002/sam
Bhat and McAvoy proposed a ‘stripping’ method to select
input variables [17]. This method requires the network
be first trained using all the input variables, and finally
the inputs irrelevant to the ANN mapping are eliminated.
Although this method leads to smaller ANNs with improved
generalization, the entire input set needs to be used to train
the network at the beginning. When the input dimensionality is large, it can be difficult to train an ANN using
the entire input vector, and the computational cost will be
high. Moreover, this method will be affected by the learning
algorithm used for ANN development.
Braddock et al. [18] put forward the input identification
methodology in multivariate case. In this method, a transfer
function is fitted to the data to determine if a Box–Cox
transformation of the data is required and to determine the
number of lagged dependent and independent variables that
should be used. However, this has the major limitation of
only capturing the inputs that are linearly correlated with
the output.
Choi B et al. utilized the genetic algorithm to optimize
the inputs to an ANN model used to estimate atmospheric
temperature [19]. However, the predicted results were
dissatisfactory and the mechanism and computation are
quite complex.
In this paper, a soft computing approach is developed
to model the relationship between yarn properties, fabric
parameters, and shear stiffness. Because only 40 samples
are available totally, the ANN model to be established must
be a small-scale one. Because there are many yarn properties affecting the shear stiffness, the yarn properties and
fabric parameters have to be ranked before modeling, so
as to find the most relevant yarn properties and fabric
parameters to fit the small-scale ANN model, that is, to
reduce the dimension of the input space. These selected
parameters will be the input variables of the small-scale
ANN model. Consequently, this soft computing approach
includes two stages. The first stage is to select yarn properties and fabric parameters as the input variables of ANN
model, which is achieved with a two-part ranking method.
The second stage is the ANN modeling of the relationship between yarn properties, fabric parameters, and shear
stiffness.
2. INPUT VARIABLE SELECTION
A method to rank the yarn properties and fabric parameters is developed in this section. This two-part method
can deal with nonlinear relationships between input and
output variables and no large number of data is required
for running it. The first part takes the human knowledge
on the shear stiffness into account (VAk ). The second part
is a data sensitivity criterion based on a distance method
(Sk ).
Chen et al.: Input Variable Selection Method
The ranking criterion is formulated as follows.
Let Xs = (xs1 , xs2 , . . . , xsk , . . . , xsn )T denotes the
input vector of all the yarn properties and the fabric parameters, and Ys = (ys1 , ys2 , . . . , ysj , . . . , ysm )T the output
vector of properties. The subscript ‘s’ indicates the sth sample [s ∈ (1, . . . , i, . . . , l, . . . , z)]. All the recorded data
have been normalized to eliminate the scale effects and the
series of data contains z samples. To rank the relevant inputs
for a given output yj , a criterion variable Fk is defined as
follows.
Fk = g1 · V Ak (xk , yj ) + g2 · Sk
[k ∈ (1, . . . , n), j ∈ (1, . . . , m)],
(1)
where g1 and g2 are two positive coefficients. The criterion
is designed for searching the best compromise between
human knowledge and data sensitivity.
The first part (VAk ) of the ranking criterion is determined
with the aid of the human knowledge [20]. As shown in
Fig. 1, the universe of discourse of yj is divided into t
equivalent intervals Cjp [p ∈ (1, . . . , t –1)]. The set Akp
is constructed with the set of input data xk that corresponds
to the output interval Cjp of yj .
The human knowledge shown in Table 1 is expressed
with linguistic sentences, such as
Rule 1: IF x1 is increasing
R(x1 , y1 ) = +1
Rule 2: IF x1 is increasing
R(x1 , y1 ) = −1
Rule 3: IF x1 is decreasing
R(x1 , y1 ) = −1
Rule 4: IF x1 is decreasing
R(x1 , y1 ) = +1
AND y1 is increasing THEN
AND y1 is decreasing THEN
AND y1 is increasing THEN
AND y1 is decreasing THEN
Then VAk can be calculated using the following formula.

t−1

1 


V
A
(x
,
y
)
=
vap
k k j


t −1


p=1




x inf = min {xsk |ysj ∈ Cjp }

 kp
s∈{1,. . .,z}


sup

 and xkp
= max {xsk |ysj ∈ Cjp }




 s∈{1,. . .,z}


1




vap = |R(xk , yj )|






2






sup
inf


×[1
+
R(xk , yj )], if xkp+1
xkp



if I = φ,


 kp

1


vap = |R(xk , yj )|

,


2




sup


inf



 ×[1 − R(xk , yj )], if xkp+1 xkp


1



vap = |R(xk , yj )|





2







|I |



,
×[1
+
R(xk , yj )] × 1 − |Ukp



|
kp





sup
sup


if xkp+1 xkp
if Ikp = φ,









1




vap = |R(xk , yj )| × [1 − R(xk , yj )]




2









 × 1 − |Ikp | , if x inf x inf
kp
kp+1
|Ukp |
(2)
Table 1. Human knowledge on the shear stiffness of
worsted fabrics.
Yarn properties and fabric parameters
Warp cover factor
Weft cover factor
Warp twist factor
Weft twist factor
Warp linear density
Weft linear density
Fiber specific surface area
Mean float
Wool percentage
Shear stiffness
+1
+1
−1
+1
+1
+1
−1
+1
−1
Fig. 1 Relationship between the input and output spaces.
Statistical Analysis and Data Mining DOI:10.1002/sam
Statistical Analysis and Data Mining, Vol. (In press)
where R(x1 , y1 ) is the relation index between input variable
x1 and output variable y1 ; va p is the human knowledge crisup
inf
terion value in the interval Cjp ; xkp
and xkp are the lower
bound (inferior limit) and upper bound (superior limit) of
set Akp , respectively; Ikp and Ukp are the intersection set
and union set generated by Akp and Akp+1 , respectively; φ
is empty set. The relation indices R in Table 1 are determined by three senior experts who are very familiar with
the relationship between yarn properties, fabric parameters,
and properties of worsted fabrics. Two of them are from
the textile mills. One is from the university laboratory. The
values of R are the consensus of the three experts.
The data sensitivity criterion Sk in Eq. (1) implies the
following two hypotheses [21]:
1. IF a small variation of an input variable corresponds
to a big variation of the output variable, THEN this
input is considered as a sensitive variable.
2. IF a big variation of an input variable corresponds to
a small variation of the output variable, THEN this
input is considered as an insensitive variable.
Therefore, according to criterion Sk , an input variable is
considered to be relevant if its small variation induces a
great variation of an output.
Tk =
z
d(yij , ylj )
,
dk (Xi , Xl )
i = l
1
(3)
(8), Method 2 utilizes the dispersion maximization decision
∗
∗
and g22
which means
principle to determine the weights g12
larger dispersion of a criterion corresponds to larger weight
∗
∗
and g22
indicates
[23]. The second subscript ‘2’ of g12
Method 2. Then the above weights are normalized using
Eq. (9). The final weights are the arithmetic average of
weights determined by the two methods, as shown in
Eqs. (10) and (11).
1
n−1
∗
=
g11
V Ak −
1
n−1
n
n
2
V Ak
k=1
,
V Ak
k=1
n
1
n
n
2
Sk
k=1
(6)
,
Sk
k=1
n
i = k
1
|V Ai − V Ak |
∗
g12
= 
2 
2 ,


 n

 
 
 n



+
−
S
|
|V Ai − V Ak |
|S
i
k 




i = k

i = k
1
1
max (Tk ) − Tk
Sk =
k∈{1,. . .,n}
max (Tk ) −
k∈{1,. . .,n}
dk (Xi , Xl )
min (Tk )
(7)
,
(4)
n
k∈{1,. . .,n}
where
=
−
(Xi , Xl )
is the Euclidean distance between Xi and Xl in the input
space. dk (Xi , Xl ) is the projection of d (Xi , Xl ) on the
axis xk . And d (yij , ylj ) is the Euclidean distance between
yi and yl of the j th output variable. The smaller the value
Tk the more relevant to yj will be the input xk . Hence, Sk is
calculated by Eq. (4) to be standardized and have the same
tendency as the human knowledge VAk (larger VAk means
more relevant).
Two methods are used to determine the weights g1
and g2 in Eq. (1). As shown in Eqs. (5) and (6), Method
1 uses the variation coefficient of VAk and Sk as their
∗
∗
and g21
, respectively. The second subscript ‘1’
weights g11
∗
∗
of g11 and g21 indicates Method 1. The principle of this
method is as follows. Larger variation coefficient means
that the corresponding criterion has stronger capability to
differentiate between samples. Hence, this criterion should
be assigned a larger weight [22]. As shown in Eqs. (7) and
d 2 (Xi , Xl )
(5)
k=1
Sk −
1
n
n
1
n
k=1
1
n
∗
g21
=
n
dk2 (Xi , Xl ), d
Statistical Analysis and Data Mining DOI:10.1002/sam
i = k
1
|Si − Sk |
∗
= 
g22
2 
2 ,


 n

 
 
 n



|V Ai − V Ak | + 
|Si − Sk |



i = k

i = k
1
1
(8)
g11 =
g12 =
∗
g11
,
g21 =
∗
g12
∗ ,
+ g22
g22 =
∗
∗
g11
+ g21
∗
g12
∗
g21
∗
∗
g11
+ g21
∗
g12
,
∗
g22
∗ ,
+ g22
(9)
g1 =
1
(g11 + g12 ),
2
(10)
g2 =
1
(g21 + g22 ).
2
(11)
Warp cover
factor
(%)
86.9
56.8
68.8
48
71.5
72.8
126
116
81.2
72.7
62.4
65.2
73.7
71
81.3
85.3
73.7
59.1
87.9
74.9
80.2
59
61.8
70.5
74.4
72.1
55.6
46.2
74.2
67.5
57
53.1
59.9
60.4
58.3
96.6
111
102
130
76.6
Sample no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
69.7
49
60.5
48.3
60.1
62.4
56.5
72.9
51.5
57.8
48.2
57.1
68
66.5
77.9
51.4
57.6
49.8
68.7
53.4
45
52.8
49.9
57.6
65.8
70.1
52.2
55.3
68.4
53.6
47.9
49.1
51.2
50.7
50.7
56.4
63.4
52
73
59.1
433
431
388
379
379
434
388
392
396
384
386
409
400
439
361
404
404
457
714
221
481
163
21
158
158
158
245
444
209
147
8
44
162
171
171
260
149
51
165
82.8
Warp twist
factor
433
431
388
379
379
407
389
392
396
384
386
408
400
439
361
386
386
457
222
419
480
163
21
418
158
158
245
477
445
147
8
44
424
424
171
261
388
0
166
395
Weft twist
factor
51.2
25
45.4
64.6
43.4
25.6
37
46.6
38.4
27.8
13.2
77
55.6
50
74
25.6
25.6
22.4
34.4
26
27.8
28.6
35.8
26
50
50
31
30.5
22.2
28.6
64.6
22.2
22.8
40
17.4
22.2
22.2
22.22
47.6
56
Warp linear
density
(tex)
51.2
25
45.4
64.6
43.4
22.22
37
46.6
38
27.8
13.2
77
55.6
50
74
20
20
22.4
34
20
27.8
28
33.4
22.22
50
50
31
25.2
20
28
64
18.52
20
40
17.4
18.52
18.52
11.11
47.6
55.56
Weft linear
density
(tex)
1.49
1.6
1.55
1.55
1.59
1.78
1.55
1.55
1.58
1.66
1.66
1.56
1.58
1.58
1.57
1.74
1.74
1.81
1.5
1.61
1.5
1.61
1.5
1.67
1.51
1.51
1.62
1.62
1.86
1.59
1.5
1.58
1.73
1.73
1.55
1.86
1.5
1.77
1.58
1.44
Fibre
specific
surface area
2.8
1
2
1
2
2
2.9
2.6
1.7
1.6
1.3
2
2.3
2
1
1.7
2
1.5
1.7
1.3
1.9
1
1
1.7
2
2
1
1
1
2.5
1
1
1
1
1
2.8
2.8
2.8
2.6
1.7
Mean float
(mm)
60
60
45
45
35
50
55
45
45
35
35
50
45
45
40
40
40
70
100
100
100
100
98
50
45
45
68
76
40
35
60
33
50
50
45
70
60
37
45
65
Wool
percentage
(%)
Experimental results of yarn properties, fabric parameters, and shear stiffness of worsted fabrics.
Weft cover
factor
(%)
Table 2.
0.93
0.68
0.52
0.60
0.74
0.60
0.80
1.83
1.16
1.02
0.48
0.59
0.83
0.78
1.51
0.85
0.62
0.62
0.51
0.87
0.65
0.56
0.87
0.72
0.92
0.77
0.67
0.66
0.39
0.33
0.52
0.67
0.90
0.79
0.91
0.57
0.71
0.50
1.09
0.56
Shear stiffness
of fabrics
[cN/cm (◦ )]
Chen et al.: Input Variable Selection Method
Statistical Analysis and Data Mining DOI:10.1002/sam
Statistical Analysis and Data Mining DOI:10.1002/sam
8
9
7
6
5
4
3
2
1
Warp cover
factor
Weft cover
factor
Warp twist
factor
Weft twist
factor
Warp linear
density
Weft linear
density
Fiber specific
surface area
Mean float
Wool
percentage
Input
VAk
0.7657
0.2909
0
0.3403
0.6453
0.6453
1
0.6453
0.6453
R
+1
+1
−1
+1
+1
+1
−1
+1
−1
0.5344
∗
g11
0.6165
∗
g12
0.4540
g11
0.4392
g12
0.4466
g1
0.0464
0.3444
0.7550
0.8325
0.8973
0.6105
1
0
0.5778
Sk
0.6428
∗
g21
0.7873
∗
g22
0.5460
g21
Data sensitivity
Ranking of yarn properties and fabric parameters.
Human knowledge
Table 3.
0.5608
g22
0.5534
g2
0.3139
0.4788
0.8644
0.7489
0.7848
0.4898
0.5534
0.1299
0.6617
Fk
8
7
1
3
2
6
5
9
4
Rank
Ranking
Statistical Analysis and Data Mining, Vol. (In press)
Chen et al.: Input Variable Selection Method
After calculating VAk , Sk , and the weights g1 , g2 , the criterion variable Fk of each input xk for a given output yj can
be determined. The larger the value Fk , the more relevant
to yj will be the input xk . Then all the Fk are ranked in a
descending order. Accordingly, the relevancies of all input
variables are in the same order as the value of Fk ranked.
Namely, the input corresponding to the first Fk of this rank
will be the most relevant input to output yj , and the like.
3. ARTIFICIAL NEURAL NETWORK MODELING
It is known that ANN models are based on experimental
data. The yarn properties and fabric parameters concerned
are the warp cover factor, weft cover factor, warp twist
factor, weft twist factor, warp linear density, weft linear
density, fiber specific surface area, mean float, and wool
percentage. Altogether there are 40 experimental runs. The
experimental program and results are shown in Table 2.
There are nine yarn properties and fabric parameters from
which inputs of the ANN model will be selected. And the
shear stiffness of fabrics will be the output.
For lack of plentiful samples, a small-scaled ANN model
is established in this study. To obtain a stable ANN, the
total number of network weights and biases cannot exceed
the number of training samples. As far as our model is
concerned, six inputs and one output are preferred. A feed
forward ANN is created. There are one hidden layer with
four neurons (more hidden neurons will cause too many
unknown weights while the number of samples is quite
limited) and one output layer with one neuron in the ANN.
The transfer functions of the hidden layer and output layer
neurons are the hyperbolic tangent function and pure linear
function, respectively.
The ANN is trained with the help of the error back propagation algorithm. In order to avoid overfitting, the Bayesian
framework is used in the training procedure. In this framework, the weights and biases of the network are assumed to
be random variables with specified distributions. The regularization parameters are related to the unknown variances
associated with these distributions. We can then estimate
these parameters using statistical techniques. It minimizes
a linear combination of squared errors and weights, then
determines the correct combination so as to produce a network that generalizes well. The process is called Bayesian
regularization [24]. In order to test the ANN model, all
the experimental data are splitted into a training set (with
39 data points) and a testing set (with 1 data point). All
combinations of 39 and 1 data points are used to train and
test the ANN. Altogether there are 39 cases being trained
and tested. Finally, the average of all the 39 ANN results
is compared with the experimental data.
4.
RESULTS AND DISCUSSION
The yarn properties and fabric parameters are selected
with regard to the shear stiffness using the method put
forward in this paper. Table 3 gives the ranking results of
the yarn properties and fabric parameters. Table 3 shows
that the weights g1 = 0.4466 for VAk and g2 = 0.5534
for Sk , which shows that the two criterions have different
importance while the data sensitivity criterion is more
important. It can be seen from Table 3 that the most relevant
yarn property is the fiber specific surface area, followed
by the warp linear density and weft linear density. Note
that the criterion Sk is insufficient to explain the ranking.
For example, considering Sk (only the measured data), the
fiber specific surface area is the fourth relevant parameter.
By adding a more general knowledge about the products
(human knowledge), the fiber specific surface area increases
to the first place.
The six inputs selected are the warp cover factor, warp
twist factor, weft twist factor, warp linear density, weft
linear density, and fiber specific surface area according to
the result of Table 3. Table 4 gives the experimental values,
predicted values, and errors for the shear stiffness. The
average error 0.209% proves the effectiveness of the ANN
model.
It can be seen from Table 4 that some of the errors
between experimental value and predicted value are a little
larger (the absolute value is nearly 12%) although the average error is small (less than 1%). The possible reasons may
be as follows. (i) The number of samples for training is
quite small. It is impossible to obtain many samples made
from different raw materials and different technologies from
a textile mill that is in stable production. In fact, it is exactly
the aim of this research to establish a soft computing-based
prediction model with few samples but tolerable predicting error for textile applications. (ii) The yarn properties
and fabric parameters are selected and several parameters
that are not very relevant to the properties investigated are
excluded from the ANN model. This will cause information loss including loss of useful information, which will
produce larger prediction errors. Small number of samples
requires small-scaled ANN models that have few input neurons. In order to decrease the prediction errors, solutions
are applied to the established ANN model. For example,
the Bayesian framework is used in the training procedure
to avoid overfitting. By comparison, it is found that the prediction errors can be much reduced than the conventional
back propagation algorithm.
There are several advantages of the input variable selection method put forward in this paper. (i) This method takes
not only the input variables but also the output variables
into account. It takes not only the experimental data itself
but also the human knowledge on the relationship between
Statistical Analysis and Data Mining DOI:10.1002/sam
Statistical Analysis and Data Mining, Vol. (In press)
Table 4.
Sample no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Average error
Results of ANN model.
Experimental value [cN/cm (◦ )]
Predicted value [cN/cm (◦ )]
Error (%)
0.93
0.68
0.52
0.60
0.74
0.60
0.80
1.83
1.16
1.02
0.48
0.59
0.83
0.78
1.51
0.85
0.62
0.62
0.51
0.87
0.65
0.56
0.87
0.72
0.92
0.77
0.67
0.66
0.39
0.33
0.52
0.67
0.90
0.79
0.91
0.57
0.71
0.50
1.09
0.56
0.934
0.718
0.575
0.619
0.781
0.659
0.812
1.856
1.140
0.974
0.478
0.599
0.881
0.692
1.501
0.785
0.603
0.619
0.457
0.834
0.650
0.526
0.870
0.751
0.917
0.790
0.636
0.663
0.392
0.358
0.480
0.708
0.872
0.756
0.902
0.615
0.713
0.519
1.084
0.562
0.452
5.588
10.558
3.133
5.473
9.800
1.500
1.426
−1.707
−4.480
−0.333
1.441
6.145
−11.269
−0.629
−7.694
−2.790
−0.210
−10.314
−4.184
−0.031
−6.089
0.034
4.306
−0.359
2.571
−5.060
0.485
0.590
8.364
−7.673
5.731
−3.078
−4.291
−0.890
7.842
0.408
3.700
−0.523
0.429
0.209
input and output variables into account. (ii) It uses the
primitive variables to rank, not their transformations as
those in the PCA. Hence, the variables have clear physical
meanings. (iii) No large number of data is required for
running this method. It also does not require the data obey
any statistical distribution. (iv) This method can deal with
nonlinear relationships between input and output variables.
(v) This method is easy to perform and does not lead to
complex computation.
Statistical Analysis and Data Mining DOI:10.1002/sam
5.
CONCLUSIONS
The relationship between yarn properties, fabric parameters, and shear stiffness of worsted fabrics is modeled using
the soft computing technique. The yarn properties and fabric parameters are selected by utilizing an input variable
selection method that can deal with nonlinear relationships
between input and output variables and no large number
of data is required for running it. The model is established
Chen et al.: Input Variable Selection Method
by using the ANN technique. The results show that the
ANN model yields accurate prediction and a reasonably
good ANN model can be achieved with relatively few
data points by integrating with the input variable selecting
method developed in this research. The results also show
that there is great potential for this research in the field of
computer-assisted design in textile technology.
Acknowledgments
Project 200761 was supported by the Foundation for
the Author of National Excellent Doctoral Dissertation of
China. Project 50506007 was supported by the National
Natural Science Foundation of China. Project 05QMX1401
was supported by the Shanghai Rising-Star Program. Project
111076 was supported by Fok Ying Tung Education Foundation.
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Statistical Analysis and Data Mining DOI:10.1002/sam