Non-Euclidean Self-Organizing Maps
This provides a more flexible framework for data analysts working with complex or hierarchical data structures, though it appears incremental as it builds on traditional SOMs.
The paper tackles the problem of Self-Organizing Maps (SOMs) being limited to Euclidean spaces by generalizing them to non-Euclidean geometries, resulting in a new degree of freedom for mapping similarities into spatial neighborhoods and enabling applications like dimension reduction and clustering in big data.
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).