Current Slide

• Let D be a training set of tuples and their associated class labels, and each tuple is represented by an n-D attribute vector X = (x1, x2, …, xn)
• Suppose there are m classes C1, C2, …, Cm.
• Classification is to derive the maximum posteriori, i.e., the maximal P(Ci|X)
• This can be derived from Bayes’ theorem

\[P(C_{i}|X)=\frac{P(X|C_{i})P(C_{i})}{P(X)}\]

• Since P(X) is constant for all classes, only 

\[P(C_{i}|X)=P(X|C_{i})P(C_{i})\]

needs to be maximized