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Kernel function can map sample in original space to high-dimensional feature space to solve the linear inseparable problem . There are several typical examples of kernel function such as linear kernel, polynomial kernel, RBF, and sigmoid kernel. Each kernel has some parameters, while RBF kernel function is strongly recommended and widely used for its performance and complexity . Linear kernels usually compute fast. LS-SVM with RBF kernel and linear function were selected in our work to compare the predictive performance with PLSR.
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Overall, LS-SVM regression models had better performance for predicting TSS than PLSR models because LS-SVM is a nonlinear regression model and it could transform the original data into a high dimension space to make linear solution . LS-SVM was capable of solving the nonlinear problem of the calibration models. LS-SVM with RBF kernel function based on 23 wavelengths with RP of 0.956 and RMSEP of 0.430 could provide the most effective TSS estimation compared to other models, while LS-SVM models with linear function had similar results with RF-PLSR models (except with full wavelengths). This consequence caused by the RBF kernel function of LS-SVM has an advantage in conducting samples in multidimensional space. In addition, linear kernel function in LS-SVM was considered as a special form of RBF kernel function .
Six mulberry fruits were used to compare the reliability of TSS distribution maps, which were predicted by three models. PLSR (Figure 7(a)) and LS-SVM with linear kernel function (Figure 7(b)) could provide clearly TSS distribution, while LS-SVM with RBF kernel function (Figure 7(c)) failed to display TSS visualization of mulberry fruits. There are four possible reasons to explain this phenomenon: (1) the special modelling way of LS-SVM with RBF kernel function, which needed to transfer the raw data into high-dimensional space, might change the original data form; (2) there were two parameters (γ, σ2) to control the predicted results of LS-SVM, which might add the complexity of LS-SVM; (3) using calibration model with 235 variables to predict a map (such a map of a mulberry was about 100 200 pixels) might produce problem of overfitting; (4) the mulberry fruit with bumpy appearance would bring the variation of spectral reflectance, which might affect the accuracy of models.