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# 4COMBINING LABEL OUTPUTS

How do we combine the outputs of the individual classifiers in the ensemble? Numerous theoretical analyses [145, 207, 235, 241, 249, 260, 394], experimental comparisons [109, 152, 222, 382, 434, 436], and reviews [392, 439] look for the answer to this question.

## 4.1 TYPES OF CLASSIFIER OUTPUTS

Consider a classifier ensemble consisting of L classifiers in the set and a set of classes Ω = {ω1, …, ωc}. Xu et al. [425] distinguish between three types of classifier outputs:

• Class labels. (The abstract level.) Each classifier Di produces a class label si ∈ Ω, i = 1, …, L. Thus, for any object to be classified, the L classifier outputs define a vector s = [s1, …, sL]T ∈ ΩL. At the abstract level, there is no information about the certainty of the guessed labels, nor are any alternative labels suggested. By definition, any classifier is capable of producing a label for x, so the abstract level is universal.
• Ranked class labels. The output of each Di is a subset of the class labels Ω, ranked in order of plausibility [184, 391]. This type is especially suitable for problems with a large number of classes, such as character, face, and speaker recognition.
• Numerical support for the classes. (The measurement level.) Each classifier Di produces a c-dimensional vector ...

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