Non-Euclidean Self-Organizing Maps

• URL: http://arxiv.org/abs/2109.11769v1
• Date: Fri, 24 Sep 2021 06:57:15 GMT
• Title: Non-Euclidean Self-Organizing Maps
• Authors: Dorota Celi\'nska-Kopczy\'nska Eryk Kopczy\'nski
• Abstract summary: We present the generalized setup for non-Euclidean SOMs. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Most data analysts take it for granted to use some subregions of a flat space as their data model; however, by the assumption that the underlying geometry is non-Euclidean we obtain a new degree of freedom for the techniques that translate the similarities into spatial neighborhood relationships. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical).

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