A Comparative Study on Discrete Discriminant Analysis through a Hierarchical Coupling Approach

Abstract

In discrete discriminant analysis the high-dimensionality problem often causes discriminant methods to perform poorly, specially in the multiclass case. The Hierarchical Coupling Model (HIERM) enables a reduction of the multiclass problem into several biclass problems embedded in a binary tree. With this approach, at each level of the tree, the basic affinity coefficient is used to select the new couple of classes among all possible forms of merging the original classes. After identifying the pair of classes to be considered, the decision rule for this biclass problem is based on the combining model that minimizes the error rate. The performance of this model leads to a considerable improvement in the misclassification error rate. Furthermore, its representation is appealing which makes it easily interpretable. In this study we propose to explore the comparison of the HIERM model with other models where the choice of the decomposition at each level of the binary tree among all possible forms of merging is made using one of the traditional similarity coefficients in Cluster Analysis. The performance of HIERM and the new models is compared on real data.