球面SOMの理論とクラスタ分析への応用(<特集>生体情報解析と複雑系科学)

概要

論文の詳細を見る
Self-Organizing Maps (SOM) is a useful tool to project multidimensional data into two- dimensional space. Usually two-dimensional rectangular plane has been used as SOM space because rectangle is appropriate to be seen. In this paper, the spherical SOM was studied on the basic property and its applications. It is shown how to arrange nodes on sphere and how to learn three dimensional object by the spherical SOM. Since each node of the spherical SOM is equivalent, less distorted map is expected. The comparison between conventional SOM and spherical one was shown and the feature was indicated here. A novel cluster analysis method is proposed too, where the multi-dimensional database is visualized as a graphical object, or Glyph. A tree structure dendrogram can be extracted from the object. To be compared with the usual dendrogram method, our proposed method has the corresponding visualization on the polygon surface as well as dendrogram. The spherical SOM was applied to clustering the design of handkerchief. It demonstrates that some inconsistencies which are seen on the 2D rectangular maps are removed on the spherical map. We can conclude that it should be the best way that a multi-dimensional data is expressed by a sphere where the phase relationship is smooth.
日本知能情報ファジィ学会の論文
2007-12-15