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

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2 BASE CLASSIFIERS

The classifiers whose decisions are combined to form the ensemble are called “base classifiers.” This chapter details some of the most popular base classifier models.

2.1 LINEAR AND QUADRATIC CLASSIFIERS

2.1.1 Linear Discriminant Classifier

Linear and quadratic classifiers are named after the type of discriminant functions they use. Let be the object to classify in one of c classes. Let be a vector with coefficients and wi0 be a constant free term. A linear classifier is any set of c linear functions, one for each class, , i = 1, …, c,

The tag of the largest gi(x) determines the class label.

2.1.1.1 Training Linear Discriminant Classifier.

A straightforward way to train a linear discriminant classifier (LDC) is shown in Figure 2.2 and detailed below:

  1. Estimate the prior probabilities for the classes. Let Ni be the number of objects in the data set Z from class ωi, i = 1, …c, and yj ∈ Ω be the class label of zjZ. Then
  2. Calculate estimates of ...

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