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A color coding scheme can be characterized by a color mapping function f: D → C that maps data values D to colors from the color palette C. In case of univariate data, each value is mapped to a single color, with multivariate data, each combination of values is mapped to a single color.
In the following we make a distinction only between qualitative (nominal) and quantitative (ordinal, interval and ratio) data values.
Associating a set of colors with a set of items to express the significance of each is called “nominal color coding.” Examples of nominal data values are: water, vegetation, and urban. There is no logical ordering in this sequence.
Color can be also used in a quantitative fashion, i.e. to convey information about ordered data set. We can distinguish here among “ordinal, interval and ratio color coding.” In ordinal coding the data values are in some way ordered, i.e., the data values can be put into a sequence but no distance is defined between data values. Examples of ordinal data values are: very bad, bad, average, good, very good. In interval coding data one can define a distance between two data values, but the zero point is arbitrary. The hue by itself can be seen as interval data values, we can say that the distance between red and yellow is 90° but we can not says that yellow is bigger than red. Periodic functions typically produce interval data values. Data sets with both positive and negative values can have a zero point representing no change, average, or expected value. In such data, deviation from zero is what is interesting. In ratio coding a zero point is therefore defined. Data values that represent the temperature are ratio data, in this case the zero point is defined at 0 Celsius degrees and we can state that a temperature of 20 Celsius degrees is twice a temperature of 10 Celsius degrees.
For nominal and ordinal data types discrete palettes must be used. For interval and ratio data one can use both discrete and continuous palettes, according to the data structure and to the visualization aims. If a discrete palette is used to code interval and ratio data, those values must be a-priori quantized into a finite number of ranges.