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Combining Pattern Classifiers: Methods and Algorithms, 2nd Edition by Ludmila I. Kuncheva

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5 COMBINING CONTINUOUS-VALUED OUTPUTS

5.1 DECISION PROFILE

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 = {ω1, ω2, …, ωc} be the set of class labels. Each classifier Di 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 di, j(x) the support that classifier Di gives to the hypothesis that x comes from class ωj. The larger the support, the more likely the class label ωj. 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.

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FIGURE 5.1 Decision profile for an input x.

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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