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To improve weak classifiers bagging and boosting could be used. These techniques are based on combining classifiers. Usually, a simple majority vote or a weighted majority vote are used as combining rules in bagging and boosting. However, other combining rules such as mean, product and average are possible. In this paper, we study bagging and boosting in Linear Discriminant Analysis (LDA) and the role of combining rules in bagging and boosting. Simulation studies, carried out for two artificial data sets and one real data set, show that bagging and boosting might be useful in LDA: bagging for critical training sample sizes and boosting for large training sample sizes. In contrast to a common opinion, we demonstrate that the usefulness of boosting does not directly depend on the instability of a classifier. It is also shown that the choice of the combining rule may affect the performance of bagging and boosting.

The Role of Combining Rules in Bagging and Boosting