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Classifiers

Classifiers . Fujinaga. Bayes (optimal) Classifier (1). A priori probabilities: and Decision rule: given and decide if and probability of error Let be the feature(s).

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Classifiers

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  1. Classifiers Fujinaga

  2. Bayes (optimal) Classifier (1) • A priori probabilities: and • Decision rule: given anddecide if and probability of error • Let be the feature(s). • Let be the class (state)- conditional probability distribution function (pdf) for ; i.e., the pdf for given that the state of nature is

  3. Bayes (optimal) Classifier (2) • Assume we know andand also we discover the value of • Using Bayes Rule: • Decide if (Maximum likelihood)

  4. Bayes (optimal) Classifier (3) A posteriori for a two class decision problem. The red region on the x axes depicts values for x for which you would decide ‘apple’ and the orange region is for ‘orange’. At every x, the posteriors must sum to 1.

  5. Fisher’s Linear Discriminant If Petal Width < 3.272 - 0.3252xPetal Length, then Versicolor If Petal Width > 3.272 - 0.3252xPetal Length, then Verginica

  6. Decision Tree If Petal Length < 2.65, then Setosa If Petal Length > 4.95, then Verginica If 2.65 < Petal Length < 4.95 then if Petal Width < 1.65 then Versicolor if Petal Width > 1.65 then Virginica

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