Multiple Dependent Variables LS-SVM Regression Algorithm and Its Application in NIR Spectral Quantitative Analysis
AN Xin1,3,XU Shuo2,ZHANG Lu-da1*,SU Shi-guang1
1. College of Science, China Agricultural University，Beijing 100094, China 2. College of Information and Electrical Engineering, China Agricultural University，Beijing 100083, China 3. School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China
Abstract：In the present paper, on the basis of LS-SVM algorithm, we built a multiple dependent variables LS-SVM (MLS-SVM) regression model whose weights can be optimized, and gave the corresponding algorithm. Furthermore, we theoretically explained the relationship between MLS-SVM and LS-SVM. Sixty four broomcorn samples were taken as experimental material, and the sample ratio of modeling set to predicting set was 51∶13. We first selected randomly and uniformly five weight groups in the interval [0, 1], and then in the way of leave-one-out (LOO) rule determined one appropriate weight group and parameters including penalizing parameters and kernel parameters in the model according to the criterion of the minimum of average relative error. Then a multiple dependent variables quantitative analysis model was built with NIR spectrum and simultaneously analyzed three chemical constituents containing protein, lysine and starch. Finally, the average relative errors between actual values and predicted ones by the model of three components for the predicting set were 1.65%, 6.47% and 1.37%, respectively, and the correlation coefficients were 0.994 0, 0.839 2 and 0.882 5, respectively. For comparison, LS-SVM was also utilized, for which the average relative errors were 1.68%, 6.25% and 1.47%, respectively, and the correlation coefficients were 0.994 1, 0.831 0 and 0.880 0, respectively. It is obvious that MLS-SVM algorithm is comparable to LS-SVM algorithm in modeling analysis performance, and both of them can give satisfying results. The result shows that the model with MLS-SVM algorithm is capable of doing multi-components NIR quantitative analysis synchronously. Thus MLS-SVM algorithm offers a new multiple dependent variables quantitative analysis approach for chemometrics. In addition, the weights have certain effect on the prediction performance of the model with MLS-SVM, which is consistent with our intuition and is validated in this study. Therefore, it is necessary to optimize weights in multiple dependent variables NIR modeling analysis.
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