Consider the canonical model of a classifier illustrated in Figure 1.9. The
degrees of support for a given input x can be interpreted in different ways, the two most common being confidences in the suggested labels and estimates of the posterior probabilities for the classes.

Let be a feature vector and Ω = {ω_{1}, ω_{2}, …, ω_{c}} be the set of class labels. Each classifier D_{i} in the ensemble outputs c degrees of support. Without loss of generality we can assume that all c degrees are in the interval [0, 1], that is, . Denote by d_{i, j}(x) the support that classifier D_{i} gives to the hypothesis that x comes from class ω_{j}. The larger the support, the more likely the class label ω_{j}. The L classifier outputs for a particular input x can be organized in a decision profile (DP(x)) as the matrix shown in
Figure 5.1.

The methods described in this chapter use DP(x) to find the overall support for each class, and subsequently label the input x in the class with the largest support. There are two ...

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