GEOG 486
Cartography and Visualization

Multivariate Representation


Multivariate representation involves using multiple visual (or other sensory) variables to represent one or more attributes on a map. In the Lesson 5 concept gallery item, Multivariate Symbols, we discussed the use of multiple visual variables to create individual multivariate symbols (i.e., symbols that represented more than one attribute within one symbol type). In this part, we consider other methods of representing multiple attributes.

One of the simplest methods for representing multivariate information is creating a composite variable from the attributes of interest. These composites are typically created using a statistical data reduction method (e.g., principle components analysis or cluster analysis) or map algebra. Although composite variables simplify the problem of cartographic representation (because there is now only one variable to represent), a major disadvantage is that we cannot retrieve information about a particular variable at a particular place (at least in the case of static paper maps).

Another widely used method for representing multivariate information is superposition of multiple symbol types within a map (e.g., displaying rates in a choropleth map and raw numbers in a graduated symbol map). This technique is particularly common in maps that use both raster and vector data. For example, one common multivariate representation involves using color hue or color value to symbolize the pixels of the raster for some attribute of interest along with a point symbol that shows some other quantity (see Figure, below). However, one drawback of superposing symbols is that as you represent more information, you may have problems with some information being obscured, as well as with the general readability of the map.

A multivariate map using superposition of multiple map symbols.
Figure This multivariate map, created with the SLICViewer, uses a combination of point, line and area symbols to represent mean annual evaporation, precipitation and temperature. In this case, the creators also used a combination of symbolization types: proportional circles, weighted isolines (isolines whose thickness varies with the data values they represent) and choropleth shading.
Credit: DiBiase, et al. 1994

One solution to the problem of obscuring information with superposed variables is to create a series of what Bertin (1977/1981) and Tufte (1983) call small multiples: sets of small maps of different variables arranged in some fashion (side-by-side, in a matrix, etc.; see Figure, below). Clearly, this type of multivariate representation should be separable (refer to Lesson 5, Multivariate Symbols for a refresher on separable vs. integral symbols), but it is less clear how well map readers can integrate information from more than one map to examine correlations.

An example of how small multiples can be used; in this case a matrix of small bivariate maps is accompanied with labels and a key.
Figure In this example, we show four (bivariate!) small multiple maps of cancer rates and health insurance. Grey areas are counties with low rates of cancers and low rates of women without insurance (i.e., high rates of women having health insurance). Dark purple areas are counties with high rates of cancer and high rates of women without insurance. Using a small multiple technique for representing this data allows us to further segment the population of women by two additional variables (cancer type and race) to see if there are different spatial patterns of cancer among those segments of the total population.

A final type of multivariate representation integrates non-visual symbolization with visual symbolization in what is called a multi-modal representation of the data. Generally, cartographers have less experience with using non-visual symbolization techniques for representing data. However, recent work by Krygier (1994) and Griffin (2001) has developed a set of sonic (i.e., sound) and a set of haptic (i.e., touch) variables for use in representing data. Although there is still significant work to be done in investigating the appropriateness and effectiveness of these non-visual variables for mapping applications, non-visual variables may have good potential for use in highly-multivariate maps where we might like to represent a variable redundantly (i.e., using more than one visual/non-visual variable) or in cases where their use may be iconic (e.g., using temperature to represent water or air temperature in the map). One example of a practical application of sound is in Fisher's (1994) uncertainty map, where he used sound to represent the classification reliability for a remotely sensed image. In his application, as the user moved his or her cursor over the image, s/he heard a sound whose pitch changed with the level of classification reliability.

Recommended Readings

If you are interested in investigating this subject further, I recommend the following:

  • Zhang, X. and M. Pazner. 2004. "The icon imagemap technique for multivariate geospatial data visualization: Approach and software." Cartography and Geographic Information Science. 31(1): 29-41.