Computational Methods for High-Dimensional Rotations in Data Visualization

摘要: Abstract There exist many methods for visualizing complex relations among variables of a multivariate dataset. For pairs quantitative variables, the method choice is scatterplot. triples 3D data rotations. Such rotations let us perceive structure three as shape point scatters in virtual space. Although not obvious, three-dimensional can be extended to higher dimensions. The mathematical construction high-dimensional rotations, however, an intuitive generalization. Whereas are thought object space, proper framework their extension better based on low-dimensional projection term “data rotations” therefore misnomer, and something along lines “high-to-low dimensional projections” would technically more accurate. To useful, need under interactive user control, they animated. We require projections static pictures but movies control. Movies, mathematically speaking one-parameter families pictures. This article about spaces . describe several algorithms dynamic projections, all idea smoothly interpolating discrete sequence projections. lend themselves implementation visual exploration tools data, such so-called grand tours, guided tours manual tours.