On the Optimum Linear Soft Fusion of Classifiers

We present new analytical developments that contribute to a better understanding of the (soft) fusion of classifiers. To this end, we propose an optimal linear combiner based on a minimum mean-square-error class estimation approach. This solution allows us to define a post-fusion mean-square-error improvement factor relative to the best fused classifier. Key elements for this improvement factor are the number of classifiers, their pairwise correlations, the imbalance between their performances, and the bias. Furthermore, we consider exponential models for the class-conditional probability densities to establish the relationship between the classifier’s error probability and the mean square error of the class estimate. This allows us to predict the reduction in the post-fusion error probability relative to that of the best classifier. These theoretical findings are contrasted in a biosignal application for the detection of arousals during sleep from EEG signals. The results obtained are reasonably consistent with the theoretical conclusions.