Least Square Support Vector Regression-Based Model for Whiteness Index of Cotton Fabric Prediction

25 The textile bleaching process uses a hydrogen peroxide (H 2 O 2 ) solution in alkali pH associated 26 with high temperature is the commonly used bleaching procedure in cotton fabric manufacture. 27 The purpose of the bleaching process is to remove the natural colour from cotton to obtain a 28 permanent white colour before dyeing or shape matching. Normally, the visual ratings of 29 whiteness on the cotton are measured by the whiteness index (WI). Notice that lesser research 30 study is focusing on chemical predictive modelling of the WI of cotton fabric than its experimental 31 study. Predictive analytics using predictive modelling can forecast the outcomes that can lead to 32 better-informed cotton quality assurance and control decisions. Up to date, limited study applying 33 least square support vector regression (LSSVR) based model in the textile domain. Hence, the 34 present study was aimed to develop the LSSVR-based model, namely multi-output LSSVR 35 (MLSSVR) using bleaching process variables to predict the WI of cotton. The predictive accuracy 36 of the MLSSVR model is measured by root mean square error (RMSE), mean absolute error 37 (MAE), and the coefficient of determination (R 2 ), and its results are compared with other 38 regression models including partial least square regression, predictive fuzzy model, locally 39 weighted partial least square regression and locally weighted kernel partial least square regression. 40 The results indicate that the MLSSVR model performed better than other models in predicting the 41 WI as it has 60% to 1209% lower values of RMSE and MAE as well as it provided the highest R 2 42 values which are up to 0.9985. 43 47 48


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The textile bleaching process uses a hydrogen peroxide (H2O2) solution in alkali pH associated 26 with high temperature is the commonly used bleaching procedure in cotton fabric manufacture. 27 The purpose of the bleaching process is to remove the natural colour from cotton to obtain a 28 permanent white colour before dyeing or shape matching. Normally, the visual ratings of 29 whiteness on the cotton are measured by the whiteness index (WI). Notice that lesser research 30 study is focusing on chemical predictive modelling of the WI of cotton fabric than its experimental 31 study. Predictive analytics using predictive modelling can forecast the outcomes that can lead to 32 better-informed cotton quality assurance and control decisions. Up to date, limited study applying 33 least square support vector regression (LSSVR) based model in the textile domain. Hence, the 34 present study was aimed to develop the LSSVR-based model, namely multi-output LSSVR Introduction relates to a white fabric's colour quality. Whiteness is defined in colorimetric terms as a colour 75 with the highest luminosity, no hue, and no saturation. The WI is calculated from the data 76 computed by colorimetric instruments such as colourimeter and spectrophotometer. The higher 77 the WI value, the greater the whiteness degree of the measured cotton (Topalovic et al. 2007). If 78 the preferred white fabric has a high reflectance, then the ideal reflectance for textile materials and shorten the processing time (Abdul and Narendra 2013). Therefore, a colorimetric analysis is 85 usually conducted to assess and investigate the bleaching procedure on the cotton samples. 86 Artificial neural networks and adaptive neuroinference systems have been used as prediction 87 models in the textile domain. However, these models require many data for model parameters 88 optimisation, and they have computational time burdens. Later, a fuzzy predictive model had been   Commission on Illumination (CIE) WI is one of the widely used colour measurement methods for 141 computing a WI to measure the degree of whiteness of bleached cotton fabric (Xu et al. 2015 Multi-output Least square support vector regression model development 152 In this study, LSSVR model is developed from the bleaching process parameters to predict the WI and a threshold value, that minimises 166 the following objective function with constraints (Eqs. 3 and 4): where  is a positive real regularised parameter, is a mapping to some high or even unlimited/ infinite dimensional Hilbert space or feature space via the nonlinear mapping 172 function  with h n dimensions, and . Unlike the single-output case, its solution to the regression 178 problem needs to be solved multiple times. Hence, the multi-output regression is much more 179 efficient than the single-output regression.

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According to Xu et al. (2013), to formulate the intuition of Hierarchical Bayes, all is assumed to be written as are small when the different outputs are same to each other, otherwise the mean , and are solved spontaneously to minimise the below objective function 186 with constraints (Eqs. 5 and 6): The Lagrangian function for the problem shown in Eqs. 5 and 6 is defined as (Eq. 7): is a matrix containing of Lagrange multipliers. The  Kuhn-Tucker conditions for optimality result the below set of linear equations (Eq. 8): ,..., , 2 1 . Hence, the following objective function (Eqs. 9 and 10) can obtain an equivalent   the respective decision function for the multiple output is (Eq. 12).
Same as the conventional LSSVR, the linear system of MLSSVR as displayed in Eq. 11 is not 215 positive define, hence solving Eq. 11 instantly is hard. But it can be reconstructed into the 216 below linear system (Eq. 13): Notice that it is easy to display S that is a positive definite matrix.

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Then, this new linear system as shown in Eq. 13 can be solved using the below steps:

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In this study, the radial basis function (RBF) kernel function adopted from Keerthi and Lin (2003) 227 as shown in Eq. 14 is used in the MLSSVR.   Table 1.  As can be seen from Eq. 18, R 2 is obtained by comparing the total of the squared errors to the total 270 of the squared deviations about its mean. R 2 uses to measure the goodness of fit between real and 271 predicted variables and its ranges is from 0 to 1 (Jaeger et al. 2017). In this study, all simulation works were performed on the same computer and software system to bleaching process using a MATLAB app that is called a fuzzy logic designer. However, this 301 method is unable to predict beyond the range of the input data. Hence, in this study, an MLSVVR 302 was developed using the bleaching process parameters to overcome the limitations of this fuzzy 303 method. Moreover, other regression models including PLSR, LW-PLSR and LW-KPLSR models 304 were also built using the same process parameters. All results from these regression models are 305 summarised in Table 2 for comparison purpose. In Table 2, the results for fuzzy method were

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The author has no conflicts of interest to declare. The author declares that she has no known 370 competing financial interests or personal relationships that could have appeared to influence the 371 work reported in this paper.