Glyph Placement for Effective Information Display

by Matthew O. Ward

ABSTRACT

The location of graphical entities such as data points, glyphs, or icons in a display can be used to convey significant information about the relations between entities. The placement problem manifests itself in many areas, including data visualization, information visualization, and screen layout, and many strategies have been developed in each domain. The goal of this talk is to identify and unite a variety of placement techniques from different disciplines, correlate techniques with implicit and explicit relations within the entities being visualized, and suggest new methods for placement and interaction with the resulting entities. I will focus on the placement of glyphs, which are graphical entities whose visual attributes are controlled by different fields of multivariate data points. However, many of the results are pertinent to the placement of icons and data points as well.

ENTITY RELATIONSHIPS

An entity is a data object consisting of a set of attributes, each of which may be of a nominal or ordinal type. Entities to be placed on a screen may or may not have quantifiable relations with each other. At a minimum, we can use the order of the entities in the file or database as an implicit linear order. Other linear orders may be derived by sorting the entities based on one or more attributes. Hierarchical ordering relations can be explicit, as in organizational charts or directory structures, or derived, such as by using clustering or partitioning algorithms. A relation which is perhaps more powerful than ordering is that of a distance or similarity metric. For M entities this would be specified as an M by M matrix, with entries indicating a degree of similarity or difference between pairs of entities. A wide range of algorithms exist for computing these similarity/difference metrics, and varying the algorithms can produce very distinct matrices.

COMMON TECHNIQUES

The most common strategy for glyph placement is either to divide the screen into M roughly equal sized regions and assign each glyph to a successive slot based on some ordering [Ward94] or use two numeric attributes of the glyph to determine a position. The former technique, while making effective use of screen space, may fail to convey relationships other than linear ordering. The latter technique can display more extensive relationships, but may suffer from occlusions and poor space utilization.

Below are some examples of existing methods for glyph/data placement, using the well-known IRIS data set. This data has 4 dimensions: petal length, petal width, cepal length, and cepal width. The data covers 3 varieties of iris, with some separation between varieties. The first example shows the IRIS data in the original order it was stored, using XmdvTool.

In this figure, the IRIS data is sorted by sepal length.

Here I use a scatterplot to show the IRIS data, with position based on 2 dimensions (sepal length vs. sepal width), using XmdvTool.

SOME CRITERIA FOR GOOD PLACEMENT

A major criterion for effectively conveying information graphically is that distortion of the actual information is minimized. Thus not only should the viewer be able to infer correct relational information (semantically similar entities should be placed near each other on the screen), but false relations (entities which are near on the screen, but not semantically close) should not be presented. Another issue is the effect of occluding entities; in most situations we would like to perceive each entity individually, which dictates against occlusion. Finally, we want to make effective use of the empty space on the screen; too much empty space may be an indication that not enough space is being allocated for glyph display, while not enough empty space may make relations, especially those involving clustering, difficult to perceive.

SOME IMPROVED PLACEMENT TECHNIQUES

For linearly ordered entities, there are several methods to convey more information using placement. VisDB [Keim94] uses a circular arrangement of sorted colored entities, with successive similar entities forming rings in the display. Similarly, the Recursive Pattern technique [Keim95] uses recursively defined raster sweeps of smaller and smaller regions, so that entities near each other in order are close to each other on the screen (this is related to space-filling curves). This technique may be extensible to handle hierarchically ordered entities as well. Hierarchically ordered entities can also be displayed using tree-maps [Johnson91], which partition space either vertically or horizontally in a recursive, alternating fashion. Another popular hierarchical technique is cone trees [Robertson91], which are 3-D trees with branches emanating in a circular fashion from parent nodes. This might be effective in the display of 3-D glyphs.

Some possible filling patterns for linear ordered glyphs, based on VisDB.

A recursive filling pattern, scanned from [Keim95].

In this figure, the IRIS data is sorted by sepal length and positioned in a spiral pattern, as in VisDB.

The IRIS data in hierarchical placement, partitioned using DySect [Andreae] and drawn using a new plotting program based on tree-maps. The method recursively divides space based on the size of membership in partitions and subpartitions, alternating horizontal and vertical orientation. The width and intensity of the boundaries show different levels of partitioning.

Entities with distance/similarity relationships can be placed using dimensionality reduction techniques such as multidimensional scaling [Bentley96] or principal components analysis. Another strategy is to perform clustering on the entities and use either a space partitioning algorithm such as tree-maps or a spring model to force separation between clusters while encouraging bonding within clusters.

Here the IRIS data is plotted using multidimensional scaling, using MAVIS.

Here the IRIS data is plotted using principal components analysis, using XmdvTool (experimental).

INTERACTIVE AND AUTOMATIC TECHNIQUES FOR DISPLAY ENHANCEMENT

There are many strategies one could use to improve the interpretability of the resulting entity placement [Ingram95]. To reduce occlusion we can apply a jitter algorithm or use a spring model to force separation. To eliminate clutter, entities can be manually deleted, made translucent, or moved to a designated ``uninteresting'' area. Finally, groups of related entities can be merged into ``mega-entities'', which can be automatically unmerged when the user zooms into a particular region of the data space.

SUMMARY

In this talk I've attempted to describe a broad spectrum of techniques for placing glyphs on a display, using the relationships explicit or implicit in the data to determine appropriate placement strategies. Future work will include implementing a single environment for experimenting with glyph placement and performing user studies to gauge the effectiveness of the various placement strategies and enhancement techniques.

REFERENCES

Andreae, P., Dawkins, B., and O'Connor, P., ``DySect: an incremental clustering algorithm,'' document included with public-domain version of the software, retrieved from http://lib.stat.cmu.edu/general/dysect.

Bentley, C.L., and Ward, M.O., ``Animating multidimensional scaling to visualize n-dimensional data sets,'' IEEE Information Visualization '96, pp. 72-73, October, 1996.

Ingram, R. and Benford, S., ``Legibility enhancement for information visualization,'' IEEE Visualization '95, pp. 209-216, October, 1995.

Johnson, B. and Shneiderman, B., ``Tree-maps: a space-filling approach to the visualization of hierarchical information structures, IEEE Visualization '91, pp. 189-194, October, 1991.

Keim, D.A., and Kriegel, H.-P., ``VisDB: database exploration using multidimensional visualization'', Computer Graphics and Applications, pp.40-49, September, 1994.

Keim, D.A., Kriegel, H.-P., and Ankerst, M., ``Recursive pattern: a technique for visualizing very large amounts of data,'' IEEE Visualization '95, pp. 279-286, October, 1995.

Robertson, G., Card, S., and Mackinlay, J., ``Cone Trees: animated 3D visualizations of hierarchical information,'' Proc. of CHI '91, pp. 189-194, 1991.

Ward, M.O., ``XmdvTool: integrating multiple methods for visualizing multivariate data,'' IEEE Visualization '94, pp. 326-333, October, 1994.

matt@owl.WPI.EDU