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0.16
0.14
K = 3
K = 4
K = 5
K = 6
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
supervision ratio (%)
Fig. 4.5
Classification error as a function of the mixture clusters and the supervision ratio
sequence and distance be different, and thus, the constructed intermediate
subspaces (with their localized patterns) are different. As a consequence of this, the
optimum clustering will be different for these two methods. Theoretically, model-
based clustering allows general patterns to be learned, while clustering using only
data objects can be biased to learn particular patterns of the given data examples.
The dendrograms of Fig.
4.6
are equivalent at the penultimate level of the
hierarchy (they found the two principal groupings of the data); however, there are
several differences in the intermediate hierarchy levels. For instance, the first three
mergings for the proposed method were between clusters: 5-6, 1-3, and 7-8; while
for the single linkage method the mergings were: 1-2, (1-2)-3, 7-10. It is clear
that the shape of the data densities favours the selection of the clusters to be
merged in the case of the proposed method, instead of the mass of data that is more
important for the single linkage method. Note that the sequence of merging for the
first method proceeds including clusters of the two larger zones of the data, while
the single linkage method focuses on only one zone in the first two mergings.
Thus, the shape of the subspaces will be quite different for the two methods at the
fourth level of the hierarchy.
4.5 Real Data Analysis: Image Processing
Local edge detectors can be extracted from natural scenes by ICA algorithms [
26
,
27
,
28
]. ICA can be used for estimating features from natural images for sparse coding
interpretation, i.e., the data vector is represented using a set of basis vectors so that
only a small number of basis vectors are activated at the same time. These vectors
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