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Fig. 7.18. Looking for a partition that is appropriate to the desired classes. The
method consists in clustering the neurons of the map by bottom-up hierarchical
classification, and testing the obtained partition with respect to the expert-classified
data
Underlying the second assumption is the hypothesis that there exists a struc-
ture on the dataset that fits the classification problem, and that it is possible
to exhibit that structure with the topological self-organization of the map.
Thus, two subsets that are represented by neighboring neurons have a strong
probability of representing observations that belong to the same class.
Of course, those assumptions are very strong. It is implicitly supposed
that a right data encoding is already known to perform the classification.
Therefore, that point must be solved in a preliminary analysis, providing
an appropriate data representation, stemming from an appropriate variable
selection and the design of a relevant coding. The effect of the coding process
on the classification result will be shown in the section devoted to applications.
Bottom-up hierarchical classification [Jain et al. 1988] may perform the
second stage of the process by appropriately clustering the neurons (see
Figs. 7.18 and 7.19).
This method computes a partition hierarchy. The various partitions of the
hierarchy are found iteratively. The initial partition is the finest one. It is made
of all the singletons of the map. From that initial partition, two subsets of the
current partition are clustered at each iteration. To select the two subsets that
are going to be clustered, a measure of the similarity between two subsets is
defined. Among all the possible subset pair, the pair that is made of the most
similar subsets, with respect to the chosen similarity criterion, is selected.
Summary of the hierarchical classification algorithm:
Hierarchical Classification Algorithm
3. Initialization . Consider the finest partition that is made by all the sin-
gletons; each neuron is allocated to a distinct subset. Choose the desired
number of subsets K .
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