Geometric Interval Classification
From Wiki.GIS.com
Originally called "Smart Quantiles", the Geometrical Interval classification method was originally introduced in the ESRI Geostatistical Analyst extension for ArcInfo.
This classification method is used for visualizing continuous data that is not distributed normally. This method was designed to work on data that contains excessive duplicate values, e.g., 35% of the features have the same value. For example, it could be used on rainfall data in which only 15 out of 100 weather stations have recorded precipitation and the rest have no recorded precipitation, so their attribute values are zero.
The Geometrical intervals classification is better than quantiles for visualizing prediction surfaces, which often do not have a normal data distribution.
The geometrical interval method is similar to a progression classification (binary, geometric, logarithmic, etc.), but it adds a coefficient. Since this method is really intended to be used as part of a data visualization process, it should be noted that it may not be very useful as a data presentation method unless there is a compelling quantitative reason. Best practices may include using a histogram with the class breaks overlaid to show the map audience what the classes mean relative to the data's distribution.[1]
Other methods of data classification used in GIS include Jenks Natural Breaks, Equal, Defined, Quantile, and Standard Deviation.
The following example illustrates geometric interval break values where the data is divided into four classes as shown in the ESRI ArcMap user interface:
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