Combining Pattern Classifiers: Methods and Algorithms, 2nd Edition

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, …, 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.

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 ...