Geoscience Reference
In-Depth Information
Fig. 4 Edge-cutting of the
minimal spanning tree
3.2.1 The Determination of the Number of Ditches
The number of ditches can be either determined with the radical law (Topfer and
Pillewizer
1966
) or defined according to the facts, and it should be smaller than the
number of the initial ditches.
3.2.2 Representation
Representation is to replace the initial clusters with new ones that are simpler.
Meanwhile the original distribution pattern should be preserved. Moreover, the
density variation should be taken into account as well. Vector quantization is used
to maintain the density distribution. It works by dividing a large set of points
(vectors) into groups and each group is represented by its centroid point. The
density matching property of vector quantization is powerful. As for the spatial
point clusters, some algorithms such as K-means and self-organized maps express
this idea excellently. K-means++ algorithm is selected in this study, considering its
success in overcoming some of the problems associated with other ways of
defining initial cluster-centers for k-means clustering (Arthur and Vassilvitskii
2007
; Shindler
2008
).
Procedures of the representation are summarized as follows: Generate the
envelope of ditches, knows as canvas in (Sandro et al.
2011
). As can be seen
shown in Fig.
5
a, the canvas is a polygon around all the segments of each ditch
cluster, reflecting the distribution range of ditches. ` Take the midpoints of each
ditch and input the midpoints of each ditch and the number of ditches into the
K-means++ algorithm. As shown in Fig.
5
b, the output would be the representative
points created by K-means++ algorithm. ยด Rebuild the new ditches according to
the
average
direction
of
the
initial
ditches,
which
extends
lines
from
the
