Visualising Clusters in High-Dimensional Data Sets by Intersecting Spheres

In this paper, we re-consider the problem of mapping a high-dimensional data set into a low-dimensional visualisation. We adopt the idea of multidimensional scaling but instead of projecting a high-dimensional point to a low-dimensional representation, we project a cluster in the high-dimensional space to a 3D-sphere. Rather than preserving distances from the high-dimensional space we aim at preserving the cluster interdependencies and try to recover them by the arrangement of the spheres. Using clusters and spheres rather than single data objects makes the method much more suitable for larger data sets. Our method can also be considered as a visual technique for cluster validity investigations. Strongly overlapping clusters or spheres in the visualisation are indicators for an unsuitable clustering result