Algorithms to improve topography preservation in self-organizing maps
Jacek M. Żurada, James S. Kirk · 2003
The self-organizing map (SOM) has become a valuable and widely-used tool for diverse applications in engineering, business, and numerous other fields. The value of the SOM lies in its ability to learn and summarize a data set, clustering the data and performing a regression upon it. This regression is intended to preserve in the SOM lattice some of the structural relationships of the data on which the map has been trained. The preservation of data structure in mappings such as the SOM is the focus of this dissertation. In preparation for the primary thrust of this document, several topics are discussed. These include a general introduction to the SOM to present terminology that will be used, and an examination of the various ways that SOM quality has been judged, particularly with respect to the way a mapping preserves and represents relationships in the data on which it is trained. Another important part of this preparatory discussion concerns what has been expected of the SOM, what has not been expected, and what can and cannot reasonably be expected. This in turn leads to a clarification of terms and an introduction to the notion of topography preservation as a worthwhile goal for mapping algorithms such as the SOM. The main body of the dissertation follows, with a proposal of six original algorithms for modifying or replacing the SOM in an effort to achieve the goal of topography preservation. The variety of these algorithms serves to illustrate the ambiguity that is inherent in the definition of topography advocated here. The usefulness of topography preservation as defined herein is further supported by a chapter describing four original illustrative applications. These demonstrate a breadth of practical uses for mappings that exhibit the quality of topography preservation.