# Quantitative Analysis of Forest Water COD Value Based on UV-vis and FLU Spectral Information Fusion
## 3 Model Algorithm  
Considering the insufficient number of sampled water bodies, we use the LSSVM algorithm to model the spectral data. To reduce the redundancy of the spectral data, we use feature selection methods to achieve data dimensionality reduction, including the SPA and CARS algorithms. The SPA algorithm is a forward iterative search method, which selects the most important wavelength point in the spectral information through projection in the vector space [28; 29]. The CARS algorithm is a feature variable selection method that combines the Monte Carlo and PLS model regression coefficients. By using the subset with the lowest root-square error of cross-validation (RMSECV) value, the best combination of variables can be efficiently found. The LSSVM algorithm replaces the inequality constraints in SVM with equality constraints, which can use fewer sample variables for model learning in high-dimensional space and solve the problem of the insufficient number of samples [30; 31]. Information fusion is the process of cognition, synthesis, and judgment of various data [32]. According to different fusion methods and levels, information fusion can be divided into three types: data-level fusion, feature-level fusion, and decision-level fusion. As a result of directly processing the original data, although data-level fusion has less information loss, the corresponding model is computationally intensive and restrictive. Feature-level data fusion extracts and processes the original data before fusion to form a new spectral matrix, thereby reducing the amount of calculation and increasing the proportion of information. Based on model fusion, decision-level data fusion makes a comprehensive decision on the final results through a voting mechanism. This approach increases the fault tolerance of the model while improving the anti-interference ability, which can be expressed as  
\[y_{pred}=k_{1}y_{modelA}+k_{2}y_{modelB} \tag{1}\]  
where \(y_{modelA}\) and \(y_{modelB}\) are the predictive results of models \(A\) and \(B\), respectively; \(k_{1}\) and \(k_{2}\) are the weight coefficients of \(y_{modelA}\) and \(y_{modelB}\) determined by the voting mechanism; and \(y_{pred}\) represents the final comprehensive decision result. The technique for order preference by similarity to the ideal solution (TOPSIS) method is a comprehensive decision-making method [33]. The objective assignment of entropy weights is used to calculate the information entropy of the index. The relative change degree of index impact on the whole system determines its weight coefficient. At the same time, the optimal and inferior solutions among the finite solutions can be obtained in the normalized original data matrix. The distances between the evaluated subjects and the two solutions are calculated separately, which can be used as a basis to evaluate the grades of the samples. Figure 1: Measured spectral data of actual water samples: (**a**) UV–vis absorbance and (**b**) FLU intensity varied with different concentrations of COD. The indicator matrix (assuming there exist \(m\) water quality samples and \(n\) concentration indicators) can be expressed as  
\[X= \begin{pmatrix}X_{11}&\cdots&X_{1n}\\ \vdots&\ddots&\vdots\\ X_{m1}&\cdots&X_{mn}\end{pmatrix} =\left\{X_{ij}\right\} \tag{2}\]  
where \(X_{ij}\) represents the \(j\)th concentration index of the corresponding \(i\)th sample. The large dispersion of \(X_{j}\) means that the indicator plays a greater role in the overall evaluation. The entropy value \(e_{j}\) and weight value \(W_{j}\) of the \(j\)th index can be calculated with the following equations:  
\[e_{j}=-\frac{1}{\ln m}\sum_{i}^{m}P_{ij}\ln P_{ij} \tag{3}\]  
\[W_{j}=\frac{1-e_{j}}{\sum_{j=1}^{m}(1-e_{j})} \tag{4}\]  
where \(P_{ij}\) indicates the proportion of the \(i\)th sample in the \(j\)th indicator and \(1-e_{j}\) corresponds to the information redundancy value of each indicator. The value of \(1-e_{j}\) is proportional to the amount of information it contains.