Optimization study on k value of K-means algorithm

In spatial clustering, the key factor to solve the problem of optimal class number is to construct a proper cluster validity function. The value of k must be confirmed in advance to exert K-means algorithm. However, it can not be clearly and easily confirmed in fact for its uncertainty. This paper recommends a distance cost function based on Euclidean distance to confirm the optimal class number, sets up a corresponding math model and designs a new optimization algorithm of k value. At the same time, the conditions of optimal solution k_opt and its up limit k_max are presented in this paper. The experiential rule which is usually expressed as k_max≤√n is theoretically proved to be reasonable. Results come from the example also show the validity of this new algorithm.