Kohonen self-organizing maps for symbolic objects

Abstract

Visualizing data in the form of illustrative diagrams and searching, in these diagrams, for structures, clusters, trends, dependencies etc. is one of the main aims of multivariate statistical analysis. In the case of symbolic data (e.g. data in form of: single quantitative value, categorical values, intervals, multi-valued variables, multi-valued variables with weights), some well-known methods are provided by suitable 'symbolic' adaptations of classical methods such as principal component analysis or factor analysis. An alternative visualization of symbolic data is obtained by constructing a Kohonen map. Instead of displaying the individual items k = 1,..., n by n points or rectangles in a two dimensional space, the n items are first clustered into a number m of mini-clusters and then these mini-clusters are assigned to the vertices of a rectangular lattice of points in the plane such that 'similar' clusters are represented by neighbouring vertices in the lattice.