Geoscience Reference
In-Depth Information
Thus, the difference between
LC
and
LR
is:
k
k
n
n
ÂÂ
n
n
f
-
f
ÂÂ
f
-
f
kj
ik
kj
ik
j
jk
=
π
1
i
ik
=
π
1
-=
-
f
f
j
=
1
i
=
1
k
+
+
k
LC
LR
=
=
(15.4)
k
k
N
N
N
= 0, there are two possibilities: classification errors are zero, or commission errors
(CE) and omission errors (OE) are the same for patch type
If
LC
-
LR
k
k
. The first possibility is normally untrue
in reality. In many situations, the second possibility is also untrue. If
k
CE
>
OE
,
LC
-
LR
> 0,
k
k
k
k
the value of %LAND of type
k
is overestimated; if
CE
<
OE
,
LC
-
LR
< 0, the value of %LAND
k
k
k
k
of type
k
is underestimated. Therefore, the components of
CE
and
OE
in Equation 15. 4 determine
k
k
the accuracy of %LAND for patch type
k
.
Mathematically,
CE
is just as follows:
k
n
Â
1
CE
=
f
kj
(15.5)
k
j
jk
=
π
OE
is just expressed as:
k
n
Â
1
OE
=
f
ik
(6)
k
i
ik
=
π
The balance between
CE
and
OE
indicates the absolute errors of area estimate for patch type
k
k
k
. The relative errors of area (REA) are then defined as:
n
n
ÂÂ
1
f
-
f
kj
ik
j
jk
=
π
i
ik
=
π
1
REA
=
¥
100
(15.7)
k
f
kk
th column in an error matrix. It represents the frequency
of sample points that are correctly classified.
According to
where
f
is an element of the
k-
th row and
k-
kk
Congalton and Green (1999), user's accuracy of type
k
(UA
) can be expressed as:
k
f
f
f
f
kk
kk
kk
UA
==
=
+
(15.8)
k
n
n
ÂÂ
1
k
+
f
f
f
kj
kk
kj
j
=
j
jk
=
π
1
and producer's accuracy of type
k
(PA
) can be expressed as:
k
