Analysis of error-reject trade-off in linearly combined multiple classifiers

In this paper, a theoretical and experimental analysis of the error-reject trade-off achievable by linearly combining the outputs of an ensemble of classifiers is presented. To this aim, the theoretical framework previously developed by Tumer and Ghosh for the analysis of the simple average rule without the reject option has been extended. Analytical results that allow to evaluate the improvement of the error-reject trade-off achievable by simple averaging their outputs under different assumptions about the distributions of the estimation errors affecting a posteriori probabilities, are provided. The conditions under which the weighted average can provide a better error-reject trade-off than the simple average are then determined. From the theoretical results obtained under the assumption of unbiased and uncorrelated estimation errors, simple guidelines for the design of multiple classifier systems using linear combiners are given. Finally, an experimental evaluation and comparison of the error-reject trade-off of the simple and weighted averages is reported for five real data sets. The results show the practical relevance of the proposed guidelines in the design of linear combiners.