A survey of multiple classifier systems as hybrid systems <s> Fuser design <s> This paper presents a method for combining classifiers that uses estimates of each individual classifier's local accuracy in small regions of feature space surrounding an unknown test sample. An empirical evaluation using five real data sets confirms the validity of our approach compared to some other combination of multiple classifiers algorithms. We also suggest a methodology for determining the best mix of individual classifiers. <s> BIB001 </s> A survey of multiple classifier systems as hybrid systems <s> Fuser design <s> A wide selection of standard statistical pattern classification algorithms can be applied as trainable fusion rules while designing neural network ensembles. A focus of the present two-part paper is finite sample effects: the complexity of base classifiers and fusion rules; the type of outputs provided by experts to the fusion rule; non-linearity of the fusion rule; degradation of experts and the fusion rule due to the lack of information in the design set; the adaptation of base classifiers to training set size, etc. In the first part of this paper, we consider arguments for utilizing continuous outputs of base classifiers versus categorical outputs and conclude: if one succeeds in having a small number of expert networks working perfectly in different parts of the input feature space, then crisp outputs may be preferable over continuous outputs. Afterwards, we oppose fixed fusion rules versus trainable ones and demonstrate situations where weighted average fusion can outperform simple average fusion. We present a review of statistical classification rules, paying special attention to these linear and non-linear rules, which are employed rarely but, according to our opinion, could be useful in neural network ensembles. We consider ideal and sample-based oracle decision rules and illustrate characteristic features of diverse fusion rules by considering an artificial two-dimensional (2D) example where the base classifiers perform well in different regions of input feature space. <s> BIB002
Some works consider the answers from a given Oracle as the reference combination model BIB001 . The Oracle is an abstract combination model, built such that if at least one of the individual classifiers provides the correct answer, then the MCS committee outputs the correct class too. Some researches used the Oracle in comparative experiments to provide a performance upper bound for classifier committee  or information fusion methods  . A simple example shows the risks of the Oracle model: assume we have two classifiers for a binary class problem, a random one and the other that always returns the opposite decision; hence the Oracle will always return the correct answer. As a consequence the Oracle model does not fit in the Bayesian paradigm. Raudys BIB002 noticed that Oracle is a kind of quality measure of a given individual classifier pool. Let us systematize methods of classifier fusion, which on the one hand could use class labels or support function, on the other hand combination rules could be given or be the results of training. The taxonomy of decision fusion strategies is depicted in Fig. 5 .