A Local Density-based Simultaneous Two-level Algorithm for Topographic Clustering

Determining the optimum number of clusters is an ill posed problem for which there is no simple way of knowing that number without a priori knowledge. The purpose of this paper is to provide a simultaneous two-level clustering algorithm based on self organizing map, called DS2L-SOM, which learn at the same time the structure of the data and its segmentation. The algorithm is based both on distance and density measures in order to accomplish a topographic clustering. An important feature of the algorithm is that the cluster number is discovered automatically. A great advantage of the proposed algorithm, compared to the common partitional clustering methods, is that it is not restricted to convex clusters but can recognize arbitrarily shaped clusters and touching clusters. The validity and the stability of this algorithm are superior to standard two-level clustering methods such as SOM+K-means and SOM+Hierarchical agglomerative clustering. This is demonstrated on a set of critical clustering problems.