A two-stage algorithm for improved topography preservation in self-organizing maps

It has been observed that the Kohonen self-organizing map (SOM) has two goals, which are pursued simultaneously in the standard training algorithm. The first goal is adequate vector quantization and the second is satisfactory preservation of topography between the input data and the output map. Vector quantization by the SOM is performed through the codebook vectors associated with vertices of the map grid, each of which represents a number of input data points. Topography preservation is achieved through the edges of the grid, which impose an output-space ordering on the (input space) codebook vectors. This paper introduces a new batch training algorithm for topography-preserving maps that approaches the two goals of the SOM independently. The algorithm is the outgrowth of a new topographical error metric that places greater emphasis on the preservation of relationships between global input data structures. Experimental results indicate that the two-stage algorithm substantially improves the preservation of global input data structures, although this improvement comes at the cost of an increase in the number of topological discontinuities on a local scale.