Geoscience Reference
In-Depth Information
considered to have the highest accuracy is used to evaluate the map of questionable accuracy.
Throughout this chapter, the term
reference map
refers to the map that is considered to have the
highest accuracy and the term
refers to the map that is compared to the reference
map. Typically, one wants to identify similarities and differences between the reference map and
the comparison map.
There are a variety of levels of sophistication by which to compare maps when they share a
common categorical variable (Congalton, 1991; Congalton and Green, 1999). The simplest method
is to compute the proportion of the landscape classified correctly. This method is an obvious first
step; however, the proportion correct fails to inform the scientist of the most important ways in
which the maps differ, and hence it fails to give the scientist information necessary to improve the
comparison map. Thus, it would be helpful to have an analytical technique that budgets the sources
of agreement and disagreement to know in what respects the comparison map is strong and weak.
This chapter introduces map comparison techniques to determine agreement and disagreement
between any two categorical maps based on the quantity and location of the cells in each category;
these techniques apply to both hard and soft (i.e., fuzzy) classifications (Foody, 2002).
This chapter builds on recently published methods of map comparison and extends the concept
to multiple resolutions (Pontius, 2000, 2002). A substantial additional contribution beyond previous
methods is that the methods described in this chapter support stratified analysis. In general, these
new techniques serve to facilitate the computation of several types of useful information from a
generalized confusion matrix (Lewis and Brown, 2001). The following puzzle example illustrates
the fundamental concepts of comparison of quantity and location.
comparison map
17.1.2
Puzzle Example
Figure 17.1 shows a pair of maps containing two categories (i.e., light and dark). At the simplest
level of analysis, we compute the proportion of cells that agree between the two maps. The
agreement is 12/16 and the disagreement is 4/16. At a more sophisticated level, we can compute
the disagreement in terms of two components: (1) disagreement due to quantity and (2) disagreement
due to location. A disagreement of quantity is defined as a disagreement between the maps in terms
of the quantity of a category. For example, the proportion of cells in the dark category in the
comparison map is 10/16 and in the reference map is 12/16; therefore, there is a disagreement of
2/16. A disagreement of location is defined as a disagreement such that a swap of the location of
a pair of cells within the comparison map increases overall agreement with the reference map. The
disagreement of location is determined by the amount of spatial rearrangement possible in the
comparison map, so that its agreement with the reference map is maximized. In this example, it
would be possible to swap the #9 cell with the #3, #10, or #13 cell within the comparison map to
increase its agreement with the reference map (Figure 17.1). Either of these is the only swap we
1 2 3 4
1 2 3 4
5 6 7 8
5 6 7 8
9 10 11 12
9 10 11 12
13 14 15 16
13 14 15 16
Comparison (forgery)
Reference (masterpiece)
Figure 17.1
Demonstration puzzle to illustrate agreement of location vs. agreement of quantity. Each map
shows a categorical variable with two categories: dark and light. Numbers identify the individual
grid cells.
