1. 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 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 < xPetal Length, then Versicolor
If Petal Width > xPetal 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