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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. REFERENCES [1] J. C. Castro, M. C. Rı́os, and C. A. Mount-Campbell, Modelling and simulation in reactive polymer processing, Model Simul Mater Sci Eng 12 (2004), S121–S149. [2] M. C. Ramesh, R. Rajamanickam, and S. Jayaraman, The prediction of yarn tensile properties by using artificial neural networks, J Text Inst 86 (1995), 459–469. [3] R. Zhu and M. D. Ethridge, Predicting hairiness for ring and rotor spun yarns and analyzing the impact of fiber properties, Text Res J 67 (1997), 694–698. [4] J. Fan and L. Hunter, A worsted fabric expert system. II. an artificial neural network model for predicting the properties of worsted fabrics, Text Res J 68 (1998), 763–771. [5] S. Ertugrul, N. Ucar, Predicting bursting strength of cotton plain knitted fabrics using intelligent techniques, Text Res J 70 (2000), 845–851. [6] S. Debnath, M. Madhusoothanan, and V. R. Srinivasamoorthy, Prediction of air permeability of needle-punched nonwoven fabrics using artifical neural network and empirical models, Indiana J Fibre Text Res 25 (2000), 251–255. [7] A. Guba, R. Chattopadhyay, and Jayadeva, Predicting yarn tenacity: a comparison of mechanistic, statistical and neural network models, J Text Inst 92 (2001), 139–145. [8] Y. Chen, T. Zhao, and B. J. Collier, Prediction of fabric enduse using a neural network technique, J Text Inst 92 (2001), 157–163. [9] K. Thirumalaiah and M. C. Deo, Hydrological forecasting using neural networks, J Hydrol Eng 5 (2000), 180–189. [10] C. Cai, D. Zhi, Z. Liu, and H. Zhang, Artificial neural network in estimation of battery state-of-charge (SOC) with nonconventional input variables selected by correlation analysis, in Proceedings of 2002 International Conference on Machine Learning and Cybernetics, Beijing, 2002, vol. 3, 1619–1625. [11] I. Drezga and S. Rahman, Input variable selection for ANNbased short-term load forecasting, IEEE Trans Power Syst 13 (1998), 1238–1244. [12] S. Gao and Y. Shan, Novel input variable selection for ANN short-term load forecasting, Autom Electr Power Syst 25 (2001), 1–4. [13] J. Utans, J. Moody, S. Rehfuss, and H. Siegelmann, Input variable selection for neural networks: application to predicting the U.S. business cycle, in Proceedings of the IEEE/IAFE 1995 Computational Intelligence for Financial Engineering, New York, April 1995, 118–122. [14] Y. Chen, M. Nguyen, and B. Park, Neural network with principal component analysis for poultry carcass classification, J Food Process Eng 21 (1998), 351–367. [15] D. Dong and T. Mcavoy, Nonlinear principal component analysis - Based on principal curves and neural networks, Comput Chem Eng 20 (1996), 65–78. [16] R. Abrahart and L. See, Investigation the role of saliency analysis with a neural network rainfall-runoff model, Comput Geosci 27 (2001), 921–928. [17] N. Bhat and T. McAvoy, Determining model structure for neural models by networks stripping, Comput Chem Eng 16 (1992), 271–281. [18] R. Braddock, M. L. Kremmer, and L. Sanzogni, Feedforward artificial neural network model for forecasting rainfall run-off, Envirometrics 9 (1998), 419–432. [19] B. Choi, T. Hendtlass, and K. Bluff, A comparision of neural network input vector selection techniques, Lecture Notes in Computer Science, Innovations in Applied Artificial Intelligence 3029, Berlin, Springer-Verlag, 2004. [20] X. Zeng, L. Koehl, M. Sanoun, M. A. Bueno, and M. Renner, Integration of human knowledge and measured data for optimization of fabric hand, Int J Gen Syst 33 (2004), 243–258. [21] X. Zeng and L. Koehl, Representation of the subjective evaluation of the fabric hand using fuzzy techniques, Int J Intell Syst 18 (2003), 355–366. [22] Y. Hu and S. He, Overall Evaluation Method, Beijing, Science press, 2000. [23] Y. Wang, Multi-attribute decision using the dispersion maximization method, China Soft Sci 13 (1998), 36–38. [24] D. J. C. MacKay, Bayesian interpolation, Neural Comput 4 (1992), 415–447. Statistical Analysis and Data Mining DOI:10.1002/sam