The Self-Organizing Map (Kohonen, 1997) is an effective and a very popular tool for data clustering and visualization. With this method, the input samples are projected into a low dimension space while preserving their topology. The samples are described by a set of features. The input space is generally a high dimensional space Rd. 2D or 3D maps are very often used for visualization in a low dimension space (2 or 3). For many applications, usually in psychology, biology, genetic, image and signal processing, such vector description is not available; only pair-wise dissimilarity data is provided. For instance, applications in Text Mining or ADN exploration are very important in this field and the observations are usually described through their proximities expressed by the “Levenshtein”, or “String Edit” distances (Levenshtein, 1966). The first approach consists of the transformation of a dissimilarity matrix into a true Euclidean distance matrix. A straightforward strategy is to use “Multidimensional Scaling” techniques (Borg & Groenen, 1997) to provide a feature space. So, the initial vector SOM algorithm can be naturally used. If this transformation involves great distortions, the initial vector model for SOM is no longer valid, and the analysis of dissimilarity data requires specific techniques (Jain & Dubes, 1988; Van Cutsem, 1994) and Dissimilarity Self Organizing Map (DSOM) is a new one. Consequently, adaptation of the Self-Organizing Map (SOM) to dissimilarity data is of a growing interest. During this last decade, different propositions emerged to extend the vector SOM model to pair-wise dissimilarity data. The main motivation is to cope with large proximity databases for data mining. In this article, we present a new adaptation of the SOM algorithm which is compared with two existing ones.
The Spread of the COVID-19 Outbreak in Brazil: An Overview by Kohonen Self-Organizing Map Networks