3 dimensional parallel coordinates plot and its use for variable selection

We propose to extend traditional 2 dimensional (2D) Parallel Coordinates plot (PCP) to the one in 3 dimensional (3D) space for showing relationships among many variables intuitively. We also illustrate that 3D PCP can be used for variable selection. In 2D PCP, we often use a brushing operation to sweep from small values to large values of one reference variable. This operation makes the relationships among the reference variable and other variables clear by using time axis. Our basic idea is to use spatial 3rd orthogonal axis instead of time. We locate line segments which show observations with respect to the values of a selected reference variable in 3D space. We show some rearrangements of order and directions of axes are useful to see the similarity between the reference variable and other variables clearly, so it can be used in the first step of variable selection. We also propose to divide values of one variable into several intervals and perform ordering with respect to the reference variable within each interval. This operation is useful to show non-linear interaction by two variables to the reference variable.