On the basis of the two-dimensional Poisson process theory and spatial point process theory, we introduced the algorithm of cluster extraction which is based on k-th order distance, aiming at determining the valid range of the algorithm. We found that the ratio of cluster and cluster's densities and the number of data both have effect on the method. But the effect of the former much bigger than that of the latter. Furthermore, we introduced the concept of weight to extend the range of the simulated data, and gave the data different weights for delineating clusters, so that the range of this algorithm can be extended.