To obtain better classification results, the outputs of an ensemble of classifiers can be combined instead of just choosing the best classifier. This combining is often done by using a simple linear combination of the outputs of the classifiers or by using order statistics (using the order in the outputs for different classes). In this paper we will show that using the normalized product of the outputs of the classifiers can be more powerful for classification performance. We will show in which cases a product combination is to be preferred and where a combination by averaging can be more useful. This will be supported by theoretical and experimental observations. 1 Introduction Certainly a very important property for a classifier is to respond meaningfully to novel patterns, i.e. the classifier generalizes [Wol94]. To obtain a network which generalizes well, one often constructs several different classifiers. Each of these classifiers have different decision boundaries and generalize...

An advantage of neural computing techniques is their ability to perform well on tasks for which conventional solutions are hard to obtain, and to generalise beyond the data on which they are trained. Artificial neural nets (ANNs) are typically trained on a sample of the data they will subsequently be required to deal with. Their performance is then assessed in terms of their ability to generalise beyond this sample, and to produce the correct answer to previously unseen items. However, although ANNs can show an impressive ability to generalise to new data, they still almost inevitably make errors on certain input patterns. Recently there has been considerable interest in the idea of improving generalisation performance by combining a number of imperfect generalisers to form a more reliable ensemble (c.f. Sharkey, 1996 for a review). Although there is convincing evidence that improved performance can be achieved, such approaches are not yet standardly adopted in neural net applications....

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