On combining classifiers using sum and product rules

This paper presents a comparative study of the performance of arithmetic and geometric means as rules to combine multiple classi®ers. For problems with two classes, we prove that these combination rules are equivalent when using two classi®ers and the sum of the estimates of the a posteriori probabilities is equal to one. We also prove that the case of a two class problem and a combination of two classi®ers is the only one where such equivalence occurs. We present experiments illustrating the equivalence of the rules under the above mentioned assumptions.