REFINING VIEWS IN N-LAND

Several techniques have been developed for refining a given view of the data (refer to LeBlanc (5) and Tipnis (19)). These are briefly presented below.

Rotation/Shearing:

It is essential that users are permitted to view the data in a non-orthogonal fashion. In N-Land there are two facilities for this. Rotation can be performed in N-D continuous space by selecting a pair of dimensions and an angle. In this case, the discretization of the dimensions remains constant, and points can move from one bin to another. Shearing, on the other hand, shifts the discrete values for each dimension, again by specifying pairs of dimensions and a shear angle. The difference is that discrete values maintain their uniqueness, which is useful for avoiding spurious gaps and overlaps in the resulting data mapping.

Binning Control:

The number and size of bins used when the range of values for a given dimension is discretized is very dependent on both the type of data being examined and the relative importance of the dimension for the particular search. In some cases, a small number of bins is satisfactory, for example corresponding to low, medium, and high values. In other situations many more bins are needed, such as for spatial dimensions. Finally, when dealing with categorical data the number of bins is often fixed. In setting the characteristics of binning for a given dimension, a histogram is plotted for that dimension to help users decide on appropriate parameters.

Overlap Control:

Whenever one discretizes a range of continuous values, there is a chance that multiple data points will map to the same location in the discrete space. Thus, N-Land permits the user to set a strategy for dealing with overlapping points. Current options include displaying the minimum, maximum, mean, or sum of the dependent variable of overlapping data points.

Dimensional Scaling:

Due to the sparseness of N-D space, it is often useful to reduce the size of the gaps between data points using various forms of scaling. N-Land supports preprocessing of each dimension (again with the assistance of a histogram) using logarithmic, exponential, and trigonometric functions.

N-D Brushing:

Brushing is a technique which has been used in high dimensional scatterplots for selecting subsets of data to be highlighted in multiple views (see Becker and Cleveland (20)). Two dimensional rectangles are specified on the screen, and any points falling into that rectangle are highlighted in other views. We have extended this concept in N-Land to permit the specification of an N-D brush, which can be used to specify a subspace surrounding an arbitrary location. The user positions the brush on the display, and any point which falls within the N-D subspace centered on this location are highlighted. Alternatively, the dependent variable may be colored to show the N-D Euclidean distance of each data point from the center of the brush. Finally, the user may choose to highlight data points whose dependent variable is within a certain range of the data point selected. N-D brushes are extremely valuable in conveying notions of spatial relationships in high dimensional data sets, and we have experimented with their use in other forms of N-D visualization (see Ward (21)).

Color Map Control:

Whenever one is using color to represent numerical or categorical information, it is important to provide users with the ability to change the color mapping. This is because color perception is both viewer-sensitive and context-sensitive. N-Land provides numerous mechanisms for adjusting the colors used for the display. Various grey-scale and color ramps may be used, or the user may select particular data points and adjust the color of all points sharing this value. The background color may also be adjusted to provide suitable contrast between space occupied by data and empty space.