Abstract
Combining multiple classifier systems (MCS’) has been shown to outperform single classifier system. It has been demonstrated that improvement for ensemble performance depends on either the diversity among or the performance of individual systems. A variety of diversity measures and ensemble methods have been proposed and studied. It remains a challenging problem to estimate the ensemble performance in terms of the performance of and the diversity among individual systems. In this paper, we establish upper and lower bounds for (a) majority voting ensemble performance with disagreement diversity measure Dis, (b) weighted majority voting performance in terms of weighted average performance and weighted disagreement diversity, and (c) plurality voting ensemble performance with entropy diversity measure ‾D . Bounds for these three cases are shown to be tight using the concept of a performance distribution pattern (PDP) for the input set. As a consequence of our previous results on diversity equivalence, (a) can be extended to several other diversity measures. Moreover, we showed in the case of (a) that when ‾ P is big enough, the ensemble performance Pm resulting from a maximum (information-theoretic) entropy PDP is an increasing function with respect to the disagreement diversity Dis. Eight experiments using data sets from various applications domains are conducted to demonstrate the complexity, richness, and diverseness of the problem in estimating the ensemble performance.