20. M. Aladjem, (1994 ) " Multiclass discriminant mappings", Signal Processing, vol. 35, 1-18. |
In [20] we extended our discriminant criteria proposed in
[15,16] for the multiclass case. Single level (one shot) and sequential
(binary tree) extensions are rigorously defined.
The single level projection optimizes the expected value
of the criteria between all pairs of the classes. The computation complexity
is analyzed and a method for reducing the calculations in the optimization
procedure is suggested. It is based on a natural selection of the significant
pairs of classes. For this purpose the weighting function of the nonparametric
scatter matrices is used as a criterion for the selection. Thus a reduction
of the computational complexity is achieved without loss of the discriminant
information. The method disregards the negligible scatter differences of
the well separated classes.
In the case of a large number of classes a binary tree projection
is recommended. An interactive algorithm for binary tree design is proposed.
It combines an automated and a manual class-composition at the nodes of
the tree. The automated procedure is based on the single link clustering
of the classes. The manual procedure is based on the visualization of the
class-configuration at the nodes of the tree.
An application of the tree projection was carried out. It concerns the diagnostic problem of cardiological diseases. The results show that the proposed tree projection is an effective tool for multiclass classifier design.
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