The Effects on Learning and Visualization of a Polyhedral Self-Organizing Map Using a Tetrahedral Approach

Abstract

Abstract A spherical self-organizing map (SSOM) based on an icosahedral geodesic dome (ICOSOM) improves the ability to visualize interactions among clusters from the input space. The SSOM reveals more information about the clusters’ properties than the original two-dimensional SOM (2D SOM) data maps, where clusters can position themselves at the edges. However, to completely visualize the spherical map, an ICOSOM requires a cumbersome data map projection using a virtual environment or cartographic projection that complicates the analyses of labels in the data map. The SSOM based on a tetrahedral geodesic dome (4HSOM) is flexible for sizing a lattice and enables the use of a more straightforward projection to obtain a data map with a complete view of the entire surface of a spherical lattice and a better analysis of the labels, such as 2D SOM projection. Nonetheless, the 4HSOM irregular lattice can interfere with the learning process and impair the visualization of the input space topographic relations on the data map. This study proposes a polyhedral SOM (PSOM) based on a tessellated tetrahedron to preserve a three-dimensional continuous space as an SSOM. The experimental results verify the quantized approximation and topological preservation and demonstrate that the PSOM with a square lattice performs better than the 4HSOM, which provides additional information about nonlinear relationships among the input data vectors. This improvement stems from the symmetrical distance among the neurons and the neighborhood function’s better fit within the square lattice, as demonstrated by experiments. We also evaluate PSOM with a rectangular lattice, ICOSOM, and 2D SOM.