The Self-Organizing Map model considers the possibility of 1D and 3D map topologies. However, 2D maps are by far the most used in practice. Moreover, there is a lack of a theory which studies the relative merits of 1D, 2D and 3D maps. In this paper a theory of this kind is developed, which can be used to assess which topologies are better suited for vector quantization. In addition to this, a broad set of experiments is presented which includes unsupervised clustering with machine learning

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... ets and color image segmentation. Statistical significance tests show that the 1D maps perform significantly better in many cases, which agrees with the theoretical study. This opens the way for other applications of the less popular variants of the self-organizing map.