## 4 Results and Discussion  
### Clustering of Spectral Polarization Data  
Since the sun elevation angle during the 4.2 field experiment was 40 degrees, data collected while the incidence angle in the laboratory is also 40 degrees are picked for analysis. The polarization information at each wavelength was divided into three combination sets:  
Figure 2: Typical target material polarization spectrum scattering characteristics test system. PSA, polarization state detector, PSG, polarization state generator, P1 and P2, linear polarizer, SF, spectral filter. combination A consisting of Stokes data, combination B consisting of Stokes and DOLP, and combination C consisting of Stokes, DOLP, and pBRDF matrix elements. Three different combination matrices were obtained, and half of the vectors in each combination matrix were selected as training set data. Samples were taken from each combined data matrix, and the cluster distance was calculated. The training set was then used in the hierarchical clustering part to run a complete clustering tree as shown in Figure 3a-c. The goal of clustering is to make data points belonging to the same cluster have a higher degree of similarity, and data points belonging to different clusters have a higher degree of difference, which means that the distance between data points in the same group is small and the distance between groups is as far as possible. Therefore, the steepness of the change in the cluster spacing and intra-cluster distance should be observed as a criterion for judging whether the classification results meet the standard. Figure 3d shows that the boundary points in combination C are steeper than those in combination A and B. From a theoretical analysis point of view, combination C contains richer data information and should have the best results. As a result, the next step is to select combination C as the data set for clustering experiments. Likewise, the cluster distance threshold for combination C when the incident angle is 40\({}^{\circ}\) is \(\varepsilon\) = 32.1446. The overall data profile will be described based on this threshold. This threshold will be used to characterize the entire data profile. The next step is to calculate the standardized Euclidean distance between all data points to form a square matrix, and set the diagonal to INF(infinity). If the distance between two points is less than the cluster distance threshold, it is established that they are members of the same cluster. The results of the contour characterization are shown in Figure 4, which indicates that the number of clusters calculated based on the cluster distance is 4; hence, the initial parameter \(K\) = 4 is substituted into the computation method described in the preceding section. All the initial parameters and overall data obtained above are then fed into the FCM algorithm for the next step of operation. Figure 3: Data training set hierarchical cluster tree and cluster distance folding line change diagram. (**a**) Combination A Stokes dataset (**b**) Combination B Stokes and DOLP dataset (**c**) Combination C Stokes, DOLP, and pBRDF matrix element dataset (**d**) Combining hierarchical cluster distance folding line change diagram with data. The data profile parameters and data matrix obtained from the previous HAC were input into the FCM algorithm to obtain the classification results. The Kosko subset measure of the algorithm results was then used to test for ambiguity, and the results were compared and analyzed. Because the amount of data was small, the FCM threshold was set to 0.01 and the maximum number of iterations to 1000. After the clustering algorithm ran and the clusters to which each data point belonged were obtained, the values of all dimensions were first normalized to facilitate observation and comparison of the abscissa.