Combining multiple classifiers by averaging or by multiplying?

In classi"cation tasks it may be wise to combine observations from di!erent sources. Not only it decreases the training time but it can also increase the robustness and the performance of the classi"cation. Combining is often done by just (weighted) averaging of the outputs of the di!erent classi"ers. Using equal weights for all classi"ers then results in the mean combination rule. This works very well in practice, but the combination strategy lacks a fundamental basis as it cannot readily be derived from the joint probabilities. This contrasts with the product combination rule which can be obtained from the joint probability under the assumption of independency. In this paper we will show di!erences and similarities between this mean combination rule and the product combination rule in theory and in practice. ( 2000 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.