Star Glyphs

Figure 2

The definition of a glyph covers a large number of techniques which map data values to various geometric and color attributes of graphical primitives or symbols [LIT:83]. Some of the many glyph representations proposed over the years include the following:
 

• Faces, where attributes such as location, shape, and size of features such as eyes, mouth, and ears are controlled by different data dimensions [CHERNOFF:73].
• Andrews glyphs, which map data to functions (e.g. trigonometric) of N variables [ANDREWS:72].
• Stars or circle diagrams, where each glyph consists of N lines emanating from a point at uniformly separated angles with lengths determined by the values of each dimension, with the endpoints connected to form a polygon [SIEGEL:72].
• Stick figure icons, where the length, orientation, and color of N elements of a stick figure are controlled by the dimensional values [GRINSTEIN:89].
• Shape coding, where each data point is represented by a rectangle which has been decomposed into N cells and the dimensional value controls the color of each cell [BED:90].

In XmdvTool, we use the star glyph pattern [SIEGEL:72]. The user can choose between either uniformly spaced glyphs or using two of the dimensions to determine the location of the glyph within the window.  Each ray of the glyph has a minimum and maximum length, determined either by the user (for glyphs with data-driven locations) or by the size of the view area (for uniformly spaced glyphs).  A key for interpreting the dimensions is included in a separate window.

Figure 2 shows an example of glyphs in XmdvTool using the same data set as in Figure 1.  The evolution of the shape over time indicates both trends and anomalies.  For example, the clear protrusion in the direction associated with cleared homicides (257 degrees) found in the earlier shapes evolves into a concavity over time.

Glyph techniques are generally limited in the number of data elements which can be displayed simultaneously, as each may require a significant amount of screen space to be viewed.  The density and size constraints of the elements, however, depend on the level of perceptual accuracy required.  Also, it can be difficult to compare glyphs which are separated in space, although if data dimensions are not being used to determine glyph locations, the glyphs can be sorted or interactively clustered on the screen to help highlight similarities and differences.  Most of the glyph techniques are fairly flexible as to the number of dimensions which can be handled, though discriminability may be affected for large values of N (greater than 20 or so).

We have extended flat star glyphs to hierarchical star glyphs. In flat star glyphs, a star glyph presents a data item. While in hierarchical star glyphs, a star glyph presents the mean of a cluster. The colorful band around it indicates the extend of the cluster. Movie 2 is a multiresolutional cluster display of hierarchical star glyphs.
 

References

[ANDREWS:72]:  Andrews, D.F..  Plots of high dimensional data. Biometrics, Vol. 28, pp. 125-136, 1972.

[CHERNOFF:73]:  Chernoff, H..  The use of faces to represent points in k-dimensional space graphically.  Journal of the American Statistical Association, Vol. 68, pp. 361-368, 1973.

[GRINSTEIN:89]:  Grinstein, G., Pickett, R., Williams, M.G. . EXVIS: an exploratory visualization environment.
Graphics Interface '89, 1989.

[LIT:83]:  Littlefield, R.J..  Using the GLYPH concept to create user-definable display formats. Proc. NCGA '83, pp. 697-706, 1983.

[SIEGEL:72]:  Siegel, J.H., Farrell, E.J., Goldwyn, R.M., Friedman, H.P..  The surgical implication of physiologic patterns in myocardial infarction shock.  Surgery, Vol. 72, pp. 126-141, 1972.

[WARD:94]:  M. Ward.  Xmdvtool: Integrating multiple methods for visualizing multivariate data.  Proc. of Visualization '94, p. 326-33, 1994.