1. Introduction to Classifiers Fujinaga

2. Bayes (optimal) Classifier (1) A priori probabilities: and Decision rule: given and decide 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 and and 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 (a feature) 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 - 0.3252 * Petal Length, then Verginica If Petal Width 4.3121 – 1.2729 * Petal Length, then Versicolor If Petal Width < 4.3121 – 1.2729* Petal Length, then Setosa

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