Abstract:An important issue in clustering analysis is to estimate the number of clusters. GS method makes reasonable estimation of the number of clusters by reference distribution, which solves the problem that other clustering methods cannot classify the data into one category, so it has better classification effect. Tibshirani R and others theatrically got the conclusion that under logarithmic concave and one dimensional case, GS method reference is uniform distribution. In view of the present situation that only a few reference distributions under different conditions had been studied, this paper put forward the best distribution of GS method under the condition of one dimensional and piecewise uniform, used the sum of squares in the class as the evaluation standard, solved the equivalent optimization problem through the Lagrange multiplier method, and obtained the result that under the above condition, uniform distribution is the maximum of the sum of squares within the class. So we get the conclusion that the reference distribution under the condition of segmental uniform distribution is still uniform for the one-dimensional data.