Growing a Hypercubical Output Space in a Self-Organizing Map

TitleGrowing a Hypercubical Output Space in a Self-Organizing Map
Publication TypeTechnical Report
Year of Publication1995
AuthorsBauer, H-U., & Villmann T.
Other Numbers970

Neural maps project data given in a (possibly high-dimensional) input space onto a neuron position in a (usually low-dimensional) output space grid. An important property of this projection is the preservation of neighborhoods; neighboring neurons in output space respond to neighboring data points in input space. To achieve this preservation in an optimal way during learning, the topology of the output space has to roughly match the effective structure of the data in the input space. We here present a growth algorithm, called the GSOM, which enhances a widespread map self-organization process, Kohonen's Self-Organizing Feature Map (SOFM), by an adaptation of the output space grid during learning. During the procedure the output space structure is restricted to a general hypercubical shape, with the overall dimensionality of the grid and its extensions along the different directions being subject of the adaptation. This constraint distinguishes the present algorithm from other, less or not constrained approaches to the problem of map topology adaptation. Depending on the embedding of neural maps in larger information processing systems, a regular neuronal grid can be essential for a successful operation of the overall system. We apply our GSOM-algorithm to three examples, two of which involve real world data. Using recently developed methods for measuring the degree of neighborhood preservation in neural maps, we find the GSOM-algorithm to produce maps which preserve neighborhoods in a nearly optimal fashion.

Bibliographic Notes

ICSI Technical Report TR-95-030

Abbreviated Authors

H.-U. Bauer and T. Villmann

ICSI Publication Type

Technical Report