This paper proposes an efficient self-organizing map algorithm based on reference point and filters. A strategy called Reference Point SOM (RPSOM) is proposed to improve SOM execution time by means of filtering with two thresholds T1 and T2. We use one threshold, T1, to define the search boundary parameter used to search for the Best-Matching Unit (BMU) with respect to input vectors. The other threshold, T2, is used as the search boundary within which the BMU finds its neighbors. The proposed algorithm reduces the time complexity from O(n2) to O(n) in finding the initial neurons as compared to the algorithm proposed by Su et al. [16] . The RPSOM dramatically reduces the time complexity, especially in the computation of large data set. From the experimental results, we find that it is better to construct a good initial map and then to use the unsupervised learning to make small subsequent adjustments.

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.