Geometric Representations for High-Dimensional Data Using a Spherical SOFM
Archana Sangole, George K. Knopf · International Journal of Smart Engineering System Design · 2003
The self-organizing feature map (SOFM) is primarily used to map high-dimensional data into low-dimensional spaces for pattern classification applications. The pre-defined connections in the SOFM lattice and the weight adaptation algorithm enable topological associations to emerge within arbitrary numeric data. The degree of association or similarity between neighboring nodes on the lattice is largely influenced by mathematical and statistical measures between the data vectors assigned to the nodes. The relationship between neighboring nodes, or cluster units, can be visually interpreted by an observer if this information is displayed as colors and/or distortions on the SOFM lattice. This paper describes how a SOFM that starts as a tessellated unit sphere can develop a closed surface topology of arbitrary N -dimensional data vectors that reflects information content as defined by the mathematical or statistical measure. Transforming the numeric data into a closed geometric form enables the information embedded in large high-dimensional data sets to be easily transferred into an immersive 3D virtual reality environment for interactive scientific data visualization. The implementation of the proposed methodology is illustrated using both high-dimensional synthetic data and the more common Fisher's Iris data.