Partitioning of Data - Spatial Mathematics: Theory and Practice through Mapping - page 130

(according to Jenks' optimization; de Smith, Goodchild, and Longley, 2012).
Simply stated, this method minimizes the sum of the variance within each of
the ranges. It attempts to find groupings and patterns inherent in the data set.
Some might view it, for ease, as equivalent to throwing a pile of papers down
the stairs and grouping the papers by step. The map in Figure 6.1 shows the
worlds' lands grouped by national area size into four different ranges with the
partition created using Jenks' method.
6.2.2 Quantile
In the quantile data range partitioning method, each range contains the same
number of observations. Note that the word “quantile” does not prescribe how
many ranges are to be chosen. If four ranges are chosen in the quantile parti-
tion, those quantiles are known as “quartiles.” If five ranges had been chosen,
they would have been “quintiles.” The word “quantile” is a derivative of the
word “quantity.” Quantiles are easy to understand, but they can be misleading.
Population counts, for example, are usually not suitable for quantile partition
because only a few places are highly populated. This distortion can be over-
come by increasing the number of data ranges, but it is better to choose a more
appropriate ranging method. Quantiles work well with linearly distributed data:
Data sets that do not have disproportionate numbers of features with similar
values. Figure 6.2 shows such a partition for the sample data set here, that of
land area by country. Most of the countries appear to be in the highest class
(the class with the most land area), but this is simply because, at this scale, the
largest countries are the most visible. The data are not linearly distributed: A
few countries have large land areas, but most countries are relatively small. The
same number of countries exists in each class, but only upon zooming in to a
larger scale can most of the countries in the other three data classes be seen.
6.2.3 Geometrical interval
This method partitions data by finding breakpoints based on class intervals that
have a geometrical series. The complex algorithm attempts to ensure that classes
have similar numbers of values and that change between the classes is close to
uniform. Ranges determined with the geometrical interval method are often
very similar to quantile ranges when the sizes of all the features are roughly the
same. Geometrical interval ranges will differ from quantile ranges if the features
are of vastly different areas, as is the case in this data set ( Figures 6.2 and
6.3 ) . In earlier times, this method was known as “smart quantiles.” This method
works farily well on data that are not distributed normally. It is a method that is
difficult to communicate via a legend or other summary materials.
6.2.4 Equal interval
The equal interval classification method partitions the range of attribute val-
ues into equal-sized subranges. Then the values are classified based on those
subranges ( Figure 6.4 ).