Show Reference: "Self-Organizing Maps on non-euclidean Spaces"

Self-Organizing Maps on non-euclidean Spaces In Kohonen Maps (1999), pp. 97-108 by Helge Ritter
@incollection{ritter-1999,
    abstract = {{INTRODUCTION}  The {Self-Organizing} Map, as introduced by Kohonen more than a decade ago, has stimulated an enormous body of work in a broad range of applied and theoretical fields, including pattern recognition, brain theory, biological modeling, mathematics, signal processing, data mining and many more [8]. Much of this impressive success is owed to the combination of elegant simplicity in the {SOM}'s algorithmic formulation, together with a high ability to produce useful answers for a wide variety of applied data processing tasks and even to provide a good model of important aspects of structure formation processes in neural systems. While the applications of the {SOM} are extremely wide-spread, the majority of uses still follow the original motivation of the {SOM}: to create dimension-reduced "feature maps" for various uses, most prominently perhaps for the purpose of data visualization. The suitability of the {SOM} for this task has been analyzed in great detail and linked to earlier},
    author = {Ritter, Helge},
    booktitle = {Kohonen Maps},
    keywords = {learning, som, topology},
    pages = {97--108},
    posted-at = {2014-03-18 15:10:52},
    priority = {2},
    title = {{Self-Organizing} Maps on non-euclidean Spaces},
    url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.3936},
    year = {1999},
    editor = {Oja, Merja and Kaski, Samuel},
    publisher = {Elsevier},
    address = {Amsterdam, The Netherlands}
}

See the CiteULike entry for more info, PDF links, BibTex etc.

One solution to border effects are SOMs with cyclic/spherical/hyper spherical/toroid topologies.