聚类分析不仅可以对考察对象按照一定标准进行分组，假如被考察对象具有地域

Cluster analysis can not only group the inspected objects according to certain standards, but if the inspected objects have regional characteristics, it can also reflect the spatial distribution pattern of the inspected objects. Cluster analysis is generally divided into two methods: K-Means Cluster cluster analysis and C-Means Cluster cluster analysis. Comparing the two, K-Means Cluster cluster analysis is currently the most commonly used and simplest cluster analysis method. . The basic principle of K-Means Cluster cluster analysis is to assume that the given sample is {x (1), …, x (n)}, and for each x( i) ∈ R n, randomly select k cluster centroid points U1 ,U2,...Uk∈R n, what K-means has to do is minimize. <br>Among them, when Γnk falls within the range of cluster k, the value is 1; otherwise, the value is 0 if it is outside the range. In general, it is very difficult to find the optimal X n and Uk through intuitive methods to minimize the value of the entire function, and it is usually obtained by multiple iterations. The specific step is to first assume that Uk is constant, and it is easy to find the optimal Uk, as long as the data points are classified to the center point closest to him to ensure that the entire function is minimized. Next, select Γnk which is constant, and then find the optimal Uk. Finally, take the derivative of Uk and assume that the entire derivative is zero, it is easy to get the smallest function value J, and Uk must be satisfied: <br>Uk is the optimal value at this time, that is, the average of all data points in cluster k value. Since each iteration takes the minimum value of J, the entire J will only decrease (or remain unchanged) without increasing, which ensures that k-means will eventually reach a minimum value. On the basis of obtaining the minimum value, through continuous clustering and merging, we will finally get the cluster grouping we want according to the initial clustering standard.

Cluster analysis can not only group the objects according to certain criteria, but also reflect the spatial distribution pattern of the objects under investigation if they have regional characteristics. Clustering analysis is generally divided into K-Means Clustering and C-Means Cluster Cluster cluster analysis. The basic principle of K-Means Cluster cluster analysis is to assume that the given sample is . . . .,... ∈ . Uk ∈ R n, and all K-means have to do is minimize it.<br>Wherein, the value is 1 when the snk is in the cluster k range, otherwise it is valued at 0 when it is outside the range. In general, it is very difficult to minimize the value of the entire function by visually finding the optimal X n and Uk, usually using multiple iterations. The concrete step is to assume that Uk is the same, and it is easy to find the optimal Uk, as long as the data points are grouped to the center point closest to him to ensure that the entire function is minimized. The next step is to choose the same, and then find the best Uk. Finally, the Uk is guided and the entire derivative is assumed to be zero, and it is easy to get the smallest function value J, while Uk is satisfied:<br>At this point Uk is the optimal value, which is the average of the data points in all cluster k. Because each iteration takes the minimum value of J, the entire J decreases (or remains the same) without increasing, which ensures that k-means eventually reaches a very small value. On the basis of the minimum value, through continuous clustering, we will eventually arrive at the clustering we want according to the initial clustering criteria.

Cluster analysis can not only group the investigated objects according to certain criteria, but also reflect the spatial distribution pattern of the investigated objects if they have regional characteristics. Cluster analysis is generally divided into two methods: K-means cluster analysis and C-means cluster analysis. Compared with the two methods, K-means cluster analysis is the most common and simple cluster analysis method. The basic principle of K-means cluster analysis is to assume that the given sample is {x (1),..., X (n)}, each x (I) ∈ R n, and randomly select k cluster centroids U1, U2,... UK ∈ R n. what K-means needs to do is to minimize.<br>Among them, when Γ The value of NK is 1 when it is in the range of cluster K, otherwise it is 0 when it is out of the range. In general, it is very difficult to find the optimal x n and UK by intuitive method to minimize the value of the whole function, which is usually solved by multiple iterations. The specific step is to assume that UK is invariant, so it is easy to find the optimal UK, as long as the data points are classified to the nearest center point to ensure that the whole function reaches the minimum. Next, choose Γ NK is invariable, and then find the optimal UK. Finally, if UK is derived and the whole derivative is assumed to be zero, it is easy to get the minimum function value J, while UK must satisfy the following conditions:<br>At this time, UK is the optimal value, that is, the average value of all the data points in cluster K. Because every iteration is to get the minimum value of J, the whole J will only decrease (or remain unchanged), but not increase, which ensures that K-means will eventually reach a minimum value. On the basis of the minimum value, through continuous clustering and merging, we will finally get the clustering group we want according to the initial clustering standard.<br>