Point Sensitivity for Radial Visualization under Dimensional Anchor Motion

Abstract

This paper extends prior work with normalized radial visualizations (NRVs) that includes the RadViz mapping onto the two-dimensional unit disk. Here we examine point sensitivity under varying assumptions about dimensional anchor motion. First, we describe the role of the barycenter of the dimensional anchors as the position where records map to under a NRV when all of their dimensional values are equal. Next, we explore the intuition that data records whose standard deviation across the dimensions is small map close to the barycenter under a NRV; such data records have low mobility. When the dimensional anchors are arranged uniformly on the RadViz circle, our distance formulation provides a preprocessing test that is sufficient for concluding that a record will lay within a circle of radius 1 2 around the barycenter. This test is independent of the ordering of the dimensional anchors on the circle. Then, for RadViz we employ a robotic motion planning analogy which utilizes the Minkowski sum to show that when some of the dimensional anchors’ positions are free to move on the unit circle, then a data record maps inside an annulus, whose center, inner and outer radii are computable. Extending the motion planning analogy, we are able to determine a dimensional anchor configuration which places a data record image point at a chosen position. To illustrate this, the Weave visualization system has been enhanced to include interactive point sensitivity features.