We present and discuss several dynamic statistical graphics tools designed to help the data analyst visually discover and formulate hypotheses about the structure of multivariate data. All tools are based on the notion of the “data space,” a representation of multivariate data as a high-dimensional (hD) space which has a dimension for each variable (column of the data) and a point for each case (row of the data). The data space is projected orthogonally onto the “visual space,” a three-dimensional space which is seen and manipulated by the data analyst. The visual space has a point-like object for each case and can have a vector-like object for each variable. The three dimensions of the visual space are orthogonal linear combinations of the variables. We discuss the notion of a “guided tour” of multivariate data space, and present guided-tour tools, including 1) 6D-rotation, a tool for dynamically rotating, in six-dimensional (6D) space, from one 3D portion of the data space to another while displaying the dynamically changing projection in the visual space; 2) hD-residualization, a tool that determines, at the user's request, the largest invisible 3D space—i.e., the largest 3D space is orthogonal to the visual space. This space is used with the visual space so that 6D-rotation can occur between two new 3D portions of the data space; 3) projection-cueing, a group of three tools that use change in object brightness as a cue to show change in aspects of the projection of objects from the data space to the visual space during hD-rotation. In addition to these tools for touring high-dimensional multivariate space, we discuss tools for manipulating the 3D visual space, and a tool for examining the relationship between two data spaces. Finally, we present a guided-tour implementation in which the user manipulates joysticks and sliders to dynamically and smoothly control the graphics tools in real time. A video suppl- - ement demonstrates the implementation.
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