|20. M. Aladjem, (1994 ) " Multiclass discriminant mappings", Signal Processing, vol. 35, 1-18.|
In  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.