A New Method to Determine Cluster Number Without Clustering for Every K Based on Ratio of Variance to Range in K-Means

In many clustering algorithms such as K-means and FCM, the cluster number K needs to be known beforehand. In this paper, we propose a new method to determine the cluster number without clustering for every K in K-means. We introduce a new statistics RVR (ratio of variance to range) and conduct Monte Carlo analysis of its characteristics. Based on the RVR, we propose an algorithm to determine the cluster number K and perform clustering utilizing it. We evaluate its effectiveness by performing a simulation test with different types of datasets; first, with real datasets, whose real number of clusters and components are known and second, with synthetic datasets. We observe a significant improvement in speed and quality of determining the cluster number and therefore clustering. Finally, we hope the proposed algorithm to be used efficiently and widely for clustering of multidimensional data.