Coloring that Reveals Cluster Structures in Multivariate Data

A method is introduced for assigning colors to displays of cluster structures of high-dimensional data, such that the perceptual differences of the colors reflect the distances in the original data space as faithfully as possible. The method consists of three parts: First the cluster structures are discovered with the Self-Organizing Map (SOM), and then a new nonlinear projection method is applied to map the cluster structures into the CIELab color space. Finally the cluster structures are visualized using the colors found by the projection. The projection method preserves best the local data distances that are the most important ones, while ensuring that the global order is still discernible from the colors, too. This allows the method to conform flexibly to the available color space. The output space of the projection need not necessarily be the color space. Projections onto, say, two dimensions can be visualized as well.