## 4 Results and Discussion
### Recognition of Different Spectral Data
#### 4.2.2 LIBS Data of _Tegillarca granosa_ Pollluted by Heavy Metals  
Figure 3b shows the LIBS data of one class of healthy and three classes of polluted _Tegillarca granosa_. The LIBS data had obvious noise signals with a relatively small amplitude, and the amplitude of some noise was less than zero. This is because the organism has both organic components and inorganic components, leading to complicated information in the general LIBS data. To improve the data-processing speed, a threshold was set as the obvious noise limit. This was defined as the absolute value of the averages of the minima of each dimension. If one specific variable of all the samples was less than this threshold (12.52), then this variable was removed. This eliminated significant noise variables and improved the algorithm's recognition and execution rates. The original spectra had 30,267 dimensions, of which 4193 remained after significant noise was removed. Figure 4: Regression coefficient of the LRSC algorithm. (In each graph, there are a total of 20 samples separated by dashed lines; the numbers above the interval represent different classes; e.g., 1 denotes the first class; A, B, C, D, and E stand for the prediction samples that belong to the first through fifth classes, respectively. Symbols 1��⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\⃝\��\⃝\⃝\⃝\⃝\��\⃝\⃝\⃝\⃝\⃝\��\⃝\⃝\��\⃝\⃝\��\⃝\⃝\�\⃝\��\⃝\⃝\�\⃝\�\⃝\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\⃝\�\�\⃝\�\�\⃝\�\⃝\�\�\⃝\�\⃝\�\�\⃝\�\⃝\�\�\⃝\�\⃝\�\�\\⃝\�\�\⃝\�\�\⃝\�\�\(a)\(b)  
The remaining spectral variables were recognized in LRSC. Each time, one sample was selected from each of the four classes of samples as the prediction samples. Based on the sparse regression coefficients of the LIBS data of different classes of _Tegillarca granosa_, as shown in Figure 4b, the \(x\) axis denotes the position of the corresponding training samples, with the areas of different classes divided by the dashed line, and the \(y\) axis represents the amplitude of the corresponding regression coefficients. As the amplitude of the LIBS data was much larger than that of the infrared spectral data, the range of the corresponding regression coefficients was also relatively large. A, B, C, and D represent the four classes of actual prediction samples. It can be seen from Figure 4b that the areas where the amplitude of the estimated prediction samples was relatively high correspond well to the actual classes of prediction samples. Figure 5b shows the residual between the estimated and actual prediction samples, where the \(x\) axis denotes the possible classes of prediction samples and the \(y\) axis stands for the residual estimate corresponding to each class of training sample. Similarly to Figure 5a, the class with the minimum residual estimate among the prediction samples was consistent with the actual class of prediction samples. However, unlike Figure 5a, the differences between classes were less significant than those of the infrared spectral data, and this is reflected in the ratio of the lowest amplitude value to the other amplitude values, so the corresponding recognition rate is lower than that of the infrared spectral data. The second column of Table 1 shows the recognition results of other common classification methods, which were inferior to the results of IR spectral data. The average accuracy of SVM and ANN was only 25%, indicating that it is almost impossible for them to correctly recognize the data. However, the recognition rate of SIMCA was only 8%, which does not comply with statistical theories. SIMCA defined four models for the four classes. When a prediction sample is projected into the four subspaces corresponding to the training samples, if we define whether the prediction sample satisfies the training set of each subspace, the prediction sample may satisfy none of the subspaces or satisfy several classes of subspaces simultaneously. When this occurs, SIMCA can make the wrong judgment, and, therefore, its recognition rate does not meet the statistical theories.