Combining Fisher Linear Discriminants for Dissimilarity Representations

Abstract

Investigating a data set of the critical size makes a classification task difficult. Studying dissimilarity data refers to such a problem, since the number of samples equals their dimensionality. In such a case, a simple classifier is expected to generalize better than the complex one. Earlier experiments [9,3] confirm that in fact linear decision rules perform reasonably well on dissimilarity representations. For the Pseudo-Fisher linear discriminant the situation considered is the most inconvenient since the generalization error approaches its maximum when the size of a learning set equals the dimensionality [10]. However, some improvement is still possible. Combined classifiers may handle this problem better when a more powerful decision rule is found. In this paper, the usefulness of bagging and boosting of the Fisher linear discriminant for dissimilarity data is discussed and a new method based on random subspaces is proposed. This technique yields only a single linear pattern recognizer in the end and still significantly improves the accuracy.