Abstract—In the field of biometric authentication, it is a promising trend to perform score fusion to improve authentication accuracy. Many empirical studies have shown the effectiveness of score fusion; however, some other researchers assert that fusion is not always beneficial. Despite considerable empirical efforts, to the best of our knowledge, the research devoted to the theoretical analysis of fusion can be found only in the paper by Poh and Bengio published in 2005. Unfortunately, we find that the variance reduction-equal error rate (VR-EER) model, which is the theoretical basis of this reference, is incorrect and the resulting conclusions are arguable. Besides, we find that the conclusions from several other empirical studies are arguable too. In this paper, using Fermat’s theorem and the connection between F-ratio and EER, we conduct a systematic theoretical study on how correlation and performances of base-experts affect fusion, giving the underlying reason why VR-EER model and the above conclusions are wrong. Contrary to these existing conclusions, we prove that provided fusion weights are selected according to our proposed criterion, the combined system will definitely be superior to all the base-experts, regardless of correlation, performances, or variances of base-experts. Experiments are carried out to validate the conclusions of ours and construct counter-examples for the existing conclusions. Index Terms—Correlation, F-ratio, optimal weight vector, performance, score fusion. I
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