Geoscience Reference
In-Depth Information
3.5 Measures for evaluation
Two measures,
Similarity
and
Connectivity
are used to evaluate each selec-
tion.
Similarity: is a critical index which has been used to evaluate the similarity
of two graphs or chemical structures (Tversky 1977; Willett 1998). Always
the higher the similarity value, the more consistent two graphs are. In the
experiment, similarity is used to measure the consistency between the
automated selection and the corresponding benchmark (i.e. the map produced
by the Hong Kong Land Department at different scales). A value can be
calculated according to Formula (4).
A
∩
B
Similarity
=
(4)
A
+
B
−
A
∩
B
where,
A
denote the length of retained roads in the selection;
B
denote
the length of retained roads in the benchmark; and
A
∩
denote the
length of their common retained roads. The maximum similarity is equal to
1.
B
Connectivity
: is one of the basic concepts in graph theory. In a graph, two
vertices
i
and
j
are connected if they have a path to connect with them.
In the experiment,
connectivity
is used to measure how well the connec-
tivity of a retained road network. It can be calculated according to Formula
(5).
∑ ∑
∈
a
ij
i
N
j
∈
N
N
;
−
j
≠
i
Connectivi
ty
=
(5)
N
(
1
where
i
a
has two values: 1 and 0. It is equal to 1 only when there are
paths from
i
to
j
. Otherwise, it is equal to 0; and
N
is the total number of
links
.
The
connectivity
value is normalized into 0 to 1. The higher the
con-
nectivity
value, the better the connectivity of a network. Only when the
connectivity
value is equal to 1, all roads within the network can be well
connected.
Figure 4
shows six schematic networks with different
connecti-
vity
values.
