Algorithm 1. K-means extraction of validation sets

Input: All-training set data AT. Number of clustering centers k

Output: Training set T. Verification set V.

1: According to the two columns of data representing coordinates in All-Training sets AT, k cluster centers are randomly selected: $\left(x_1,y_1\right),\cdots ,\left(x_k,y_k\right)$. Define an empty list KC.

2: Put the point $\left(x_j,y_j\right)$ into KC, where $j\in \left(1,k\right)$.

3: for $\left(x_i,y_i\right)$ to the last two columns of data in AT do

4:   for $\left(x_j,y_j\right)$ to KC do

5:      Repeat the process until the clustering center remains unchanged

6:         {

7:           //For each example, calculate the class it should belong to.

8:          $c^{\left(i\right)}:=\arg \underset{j}{min}{\Vert \left(x_i,y_i\right)-\left(x_j,y_j\right)\Vert }^2$

9:         //For each class, recalculate its cluster center instead of the cluster center at the original location.

10:         $\left(x_j^{\prime },y_j^{\prime }\right):=\frac{{\Sigma }_n^{i=1} 1{\{c^{\left(i\right)}=j\}}^{\left(i\right)}}{{\Sigma }_n^{i=1} 1\{c^{\left(i\right)}=j\}}$

11:         Put the point $\left(x_j^{\prime },y_j^{\prime }\right)$ into KC.

12:       }

13:    end for

14: end for

15://The sample points closest to the cluster center are placed in the validation set V.

16: $I=\arg \underset{i}{min}\sqrt{{(x_i-x_j^{\prime })}^2+{(y_i-y_j^{\prime })}^2}$

17: Put the data in row I of AT into V.

18: Delete row I data from AT.

19: T←AT

20: return T, V