Research Methodology - Historical Land Use/Land Cover Classification Using Remote Sensing - page 149

Reference truth data

Class 1 ∑

Class 2 Class c

Class 1

Class 2

Class c

N

∑

Fig. 5.63 Explanation of the error matrix approach (Source modified from Congalton and Green

1999 )

Let, for a (l-class) classification problem, (N) be the total number of reference
samples. The corresponding confusion matrix is illustrated in Fig. 5.63 . The
number of samples that are classified as class/xi (i = 1,2,…,l)/and belong to land
cover class/xj (j = 1,2, …,l)/are described by ( n ij ), for example, (n 11 ) denotes the
number of samples that belongs to class (1) and correctly assigned to class (1),
whereas (n 21 ) defines the samples belonging to class (1), but incorrectly classified
to class (2). The diagonal cells (n cc ) (the highlighted elements in Fig. 5.63 ) of the
error matrix contain the number of correctly classified samples (Congalton and
Green 1999 ), while the off-diagonal cells represent the disagreement between the
classified image and the ground truth data. The overall accuracy is calculated by
their sum (the diagonal observations) divided by the total number of samples (N)
(all observations included in the error matrix):
Overall accuracy ¼ P c ¼ 1 n cc
N
Generally, the individual LULC-class that accounts for a large rate of the study/
testing area, might be classified with a high accuracy using an individual classi-
fication algorithm, which creates an alignment in overall accuracy. Therefore, it is
necessary to consider the individual class accuracies to avoid the alignment. Class-
specific accuracies can be created based on the confusion matrix (i.e., producer and
user accuracy). It can be also used to create the corresponding error rates. ''An
error of omission is to exclude a sample from a class in which it originally belongs
(a misclassification error is an omission from the correct class). A commission
error on the other hand assigns a sample to a wrong class (a misclassification error
is a commission into another class). Consequently, each error is an omission from
the correct class and a commission to a wrong class. The producer accuracy, that is
a measure of error of omission'' (Story and Congalton 1986 ), for class (c) is