Image Processing Reference
In-Depth Information
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FIGURE 16.3
A dendrogram obtained starting from 20 elements or clusters.
resulting in an N
N array. After this operation, the two nearest clusters are
merged together, and a new distance matrix is computed. This operation ends
when there is only one cluster remaining (see Figure 16.3) Different clusters can
be identified by this method depending upon the level of the dendrogram chosen:
in order to decide at which level to stop and how many clusters to consider, it is
possible to find a good compromise between between-class inertia minimization
and the number of classes. Hierarchical clustering methods differ in the way the
cluster distance is computed: in single-linkage methods, the distance between
two clusters is computed as the minimum of all the distances of any element of
the first cluster to any element of the second. in complete-linkage methods, the
distance is measured as the maximum distance of all the distances of any element
of one cluster to any element of the other. The complete-linkage method finds
compact tightly bound clusters, whereas the single-linkage method finds clusters
that are elongated and suffers a chaining effect. Dimitriadou et al. [24] found that
the complete-linkage method outperformed the single-linkage method. The reason
is the large number of clusters that do not show any activation and cause a bias
in the clusters. In Reference 15 the problem of spatial separation of overlapping
clusters in single-linkage methods was addressed, and a sharpening procedure of
the dendrogram was proposed. Another criterion is the Ward method [50], which
consists in merging every possible cluster pair and choosing the one that mini-
mizes information loss. In order to estimate this quantity, the error sum of squares,
defined as
×
∑
ESS C
i
()
=
(
xm
−
)
(16.8)
i
xC
i
∈
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