## 3 Study Methods and Evaluation Process
### Fuzzy C-Means Clustering Algorithm
#### 3.3.2 Method of Implementation  
In this paper, the fuzzy C-mean clustering algorithm is written based on Python, and the main iterative steps are as follows.  
1. Determine the number of classifications, the dimensionality, the value of the fuzzy index m, and the number of iterations;
2. Initialize an affiliation matrix U that satisfies normalization and sums to 1;
3. Calculate the clustering center C based on the initialized U;
4. update the affiliation U using a weighted Euclidean distance based on the value of C;
5. Repeat steps 3 and 4 until the number of iterations is reached;
6. Determine the classification result based on the maximum affiliation;Consider the clustering complete when the clustering centers of the samples no longer change.  
Establishing a Fuzzy C-Mean Clustering Model  
Although thousands of calculation tools are available in GIS, this paper uses fuzzy C means clustering and improved weighted Euclidean distance, and raster analysis cannot be performed directly in GIS. It is complicated to build a toolbox by toolbox, so this study uses a simple method of exporting raster point data and calculating it in Python. Assuming that there are \(K\) evaluation indicators in the underground space resource development evaluation system \(U\), and each indicator level raster map has \(N\) identical rasters, the \(K\times N\) matrix of the extracted point data attributes is as follows.  
\[U=\begin{bmatrix}U_{1,1}&U_{1,2}&\dots&U_{1,K}\\ U_{2,1}&U_{2,2}&\dots&U_{2,K}\\ \dots&\dots&\dots&\dots\\ U_{N,1}&U_{N,2}&\dots&U_{N,K}\end{bmatrix} \tag{9}\]  
An improved fuzzy C clustering algorithm was written by Python, and since the numbers in Python start from 0, if we assume that the rubric set is divided by four levels and each raster classification result is Vi, then Vi can only be 0, 1, 2, 3. The raster map of all evaluation indexes is rasterized to points, and then the data is matched with the spatial location of the raster according to the point number, and the data is imported into the Python model for calculation, and the calculated results are imported into the form of point data, matched with the point number, and finally, the raster map of suitability levels is generated based on the MAX principle in the point-to-raster, which ensures that the generated raster map is identical to the original raster Finally, the raster map is generated based on the MAX principle in point-to-raster, ensuring that the generated raster map is identical to the center point and raster position of the original raster.  
In the Raster point element process, a point is created in the output element class for each image element of the input raster dataset. These points will be positioned at the center of the image element they represent. No data image element will not be converted to a point, and the field parameters can be selected as input raster dataset attribute fields that can become attributes of the output element class. The point element number is the same for all evaluation metric raster maps, and when converting points to raster, the value of the point within each raster image is usually assigned to the corresponding raster image, and the No Data value is assigned to raster images that do not contain points. If multiple points are found in a raster image, the value of the first point encountered is assigned to that raster image. To ensure the accuracy of the element point to raster conversion, the size of the original raster element is captured during the conversion, and the element with the most common attribute in the value field is assigned to the element according to MOST_FREQUENT in cell_assignment, i.e., if there are multiple elements in the element. Only the raster centroid elements are in the raster, so the accuracy of the transformed raster is guaranteed.