Self-Organizing Map (SOM) is a powerful tool for the exploratory of clustering methods. Clustering is the most important task in unsupervised learning and clustering validity is a major issue in cluster analysis. In this paper, a new clustering validity index is proposed to generate the clustering result of a two-level SOM. This is performed by using the separation rate of inter-cluster, the relative density of inter-cluster, and the cohesion rate of intra-cluster. The clustering validity index is proposed to find the optimal numbers of clusters and determine which two neighboring clusters can be merged in a hierarchical clustering of a two-level SOM. Experiments show that, the proposed algorithm is able to cluster data more accurately than the classical clustering algorithms which is based on a two-level SOM and is better able to find an optimal number of clusters by maximizing the clustering validity index.

The structural characteristics of clusters are investigated in the partitioning process. Two partition functions, which show opposite properties around the optimal cluster number, are found and a new cluster validity index is presented based on the combination of these functions. Some properties of the index function are discussed and numerical examples are presented.