I. Introduction
The topologies of data distributions are very important for data description. Usually, it is not easy to find a description that can give us a precise understanding of the topologies for general distributions. The Self-Organizing Map (SOM) [14] is a neural network algorithm which is based on unsupervised learning and combines the tasks of vector quantization and data projection. It is a powerful tool in several problematic domains, such as data mining/knowledge exploration, vectors quantification and data clustering tasks [6][7][11][13][15][17]. It is capable of projecting high-dimensional data onto a low dimensional space (one, two or three dimensional structure), with good neighborhood preservation between the two spaces. However, due to the static structure of SOM, the neighborhood preservation cannot always lead to perfect topology preservation. Since, SOM algorithm has needed to fix the size of the grid at the beginning of the training process. This includes the topology as well as the number of nodes. So, Ref. [19] proposes limited using data topology in SOM representation that indicates topology violations and data distribution.