Interactive Design of Multidimensional Data Projection Layout

Abstract

Projection methods support effective visualizations of multidimensional data. Linear projections are an importantsubclass, as they allow for interactive visual exploration of the data space and feature sensitivity analysis. Theuser interaction is usually based on an iterative modification of the projection matrix elements, for example, by theuse of a star coordinate widget. However, such interaction mechanisms become inefficient with increasing numberof dimensions. We propose to adapt the projection matrix by allowing the user to directly operate on the projectiondomain. The desired configuration of the projection layout is obtained by adjusting the positions of (freely chosen)control points. The update of the projection matrix is performed according to the interactive modifications bycomputing a least-square solution of a linear equation system. Changes can be tracked easily using animation. Weapply our method to classified multidimensional data and demonstrate that our approach allows for an intuitiveand effective design of projections with desired properties like improved class segregation or reduced clutter.