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Classification Is to Derive the Maximum Posteriori
- 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
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