Within GIS software, univariate classification facilities are found as tools to: aid in the production of choropleth or thematic maps; explore untransformed or transformed datasets; analyse (classify and re-classify) image data (see further, Section 4.2.12.3); and display continuous field data. In the majority of cases these procedures perform classification based purely on the input dataset, without reference to separate external evaluation criteria.

In almost all instances the objects to be classified are regarded as discrete, distinct items that can only reside in one class at a time (sometimes referred to as hard classification). Separate schemes exist for classifying objects that have uncertain class membership (soft or fuzzy classification) and/or unclear boundaries (as discussed briefly in Section 4.2.13.4), or which require classification on the basis of multiple attributes (see Section 4.2.12.2). Typically the attributes used in classification have numerical values that are real or integer type. In most instances these numeric values represent interval or ratio-scaled variables. Purely nominal data are effectively already classified (see, for example, Figure 4‑20 in which each zone has been assigned a unique colour from a pre-selected palette; and see Section 2.2.2 for a brief discussion of commonly used scales).

Table 4‑5 provides details of a number of univariate classification schemes together with comments on their use. Most of the main GIS packages provide classification options of the types listed, although some (such as the box and percentile methods) are only available in a limited number of software tools (e.g. GeoDa). A useful variant of the box method, known as hybrid equal interval, in which the inter-quartile range is itself divided into equal intervals, does not appear to be implemented in mainstream GIS packages. Schemes that take into account spatial contiguity, such as the so-called minimum boundary error method described by Cromley (1996), also do not appear to be readily available as a standard means of classification.

Brewer and Pickle (2002) examined many of these methods, with particular attention being paid to ease of interpretation and comparison of map series, e.g. mapping time series data, for example of disease incidence by health service area over a number of years. They concluded that simple quantile methods were amongst the most effective, and had the great advantage of consistent legends for each map in the series, despite the fact that the class interval values often vary widely. They also found the schemes that resulted in a very large central class (e.g. 40%+) were more difficult to interpret.

In addition to selection of the scheme to use, the number of breaks or intervals and the positioning of these breaks are fundamental decisions. The number of breaks is often selected as an odd value: 5, 7 or 9. With an even number of classes there is no central class, and with a number of classes less than 4 or 5 the level of detail obtained may be too limited. With more than 9 classes gradations may be too fine to distinguish key differences between zones, but this will depend a great deal on the data and the purpose of the classification being selected. In a number of cases the GIS package provides linked frequency diagrams with breaks identified and in some cases interactively adjustable. In other cases generation of frequency diagrams should be conducted in advance to help determine the ideal number of classes and type of classification to be used. For data with a very large range of values, smoothly varying across a range, a graduated set of classes and colouring may be entirely appropriate. Such classification schemes are common with field-like data and raster files. Continuous graded shading of thematic maps is also possible, with some packages, such as Manifold’s Thematic Formatting facilities providing a wide range of options that reduce or remove the dependence on formal class boundaries.

Positioning of breaks may be pre-determined by the classification procedure (e.g. Jenks Natural breaks), but these are often manually adjustable for some of the schemes provided — this is particularly useful if specific values or intervals are preferred, such as whole numbers or some convenient values such as 1000s, or if comparisons are to be made across a series of maps. In some instances options are provided for dealing with zero-valued and/or missing data prior to classification, but if not provided the data should be inspected in advance and subsets selected prior to classification where necessary. Some authors recommend that maps with large numbers of zero or missing data values should have such regions identified in a class of their own.

The Jenks method, as implemented in a number of GIS packages such as ArcGIS, is not always well-documented so a brief description of the algorithm follows (Figure 4‑21). This description also provides an initial model for some of the multivariate methods described in subsection 4.2.12.2.