# 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 = {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*gives to the hypothesis that

_{i}**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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