Interactive Visualization and Navigation in Large Data Collections using the Hyperbolic Space

We propose the combination of two recently introduced methods for the interactive visual data mining of large collections of data. Both, Hyperbolic Multi-Dimensional Scaling (HMDS) and Hyperbolic Self-Organizing Maps (HSOM) employ the extraordinary advantages of the hyperbolic plane (H2): (i) the underlying space grows exponentially with its radius around each point ideal for embedding high-dimensional (or hierarchical) data; (ii) the Poincaré model of the IH exhibits a fish-eye perspective with a focus area and a context preserving surrounding; (iii) the mouse binding of focus-transfer allows intuitive interactive navigation. The HMDS approach extends multi-dimensional scaling and generates a spatial embedding of the data representing their dissimilarity structure as faithfully as possible. It is very suitable for interactive browsing of data object collections, but calls for batch precomputation for larger collection sizes. The HSOM is an extension of Kohonen’s Self-Organizing Map and generates a partitioning of the data collection assigned to an IH tessellating grid. While the algorithm’s complexity is linear in the collection size, the data browsing is rigidly bound to the underlying grid. By integrating the two approaches we gain the synergetic effect of adding advantages of both. And the hybrid architecture uses consistently the IH visualization and navigation concept. We present the successfully application to a text mining example involving the Reuters-21578 text corpus.