Visualization of randomly ordered numeric data sets using spherical self-organizing feature maps

Abstract

Scientific data visualization requires a variety of mathematical techniques to transform multivariate data sets into simple graphical objects, or glyphs, that provide scientists and engineers with a clearer understanding of the underlying system behaviour. The spherical self-organizing feature map (SOFM) described in this paper exploits an unsupervised clustering algorithm to map randomly organized N-dimensional data into a lower three-dimensional (3D) space for visual pattern analysis. Each node on the spherical lattice corresponds to a cluster of input vectors that lie in close spatial proximity within the original feature space, and neighbouring nodes on the lattice represent cluster centres with a high degree of vector similarity. Simple metrics are used to extract associations between the cluster units and the input vectors assigned to them. These are then graphically displayed on the spherical SOFM as either surface elevations or colourized facets. The resulting colourized graphical objects are displayed and manipulated within 3D immersive virtual reality (IVR) environments for interactive data analysis. The ability of the proposed algorithm to transform arbitrarily arranged numeric strings into unique, reproducible shapes is illustrated using chaotic data generated by the Lozi, Hénon, Rössler, and Lorenz attractor functions under varying initial conditions. Implementation of the basic data visualization technique is further demonstrated using the more common Wisconsin breast cancer data and multi-spectral satellite data.