Data Mining

3

Naïve Bayes Classifier

A naïve Bayes classifier is based on the Bayes theorem. Hence, this chapter first reviews the Bayes theorem and then describes naïve Bayes classifier. A list of data mining software packages that support the learning of a naïve Bayes classifier is provided. Some applications of naïve Bayes classifiers are given with references.

3.1    Bayes Theorem

Given two events A and B, the conjunction (∧) of the two events represents the occurrence of both A and B. The probability, P(A ∧ B) is computed using the probability of A and B, P(A) and P(B), and the conditional probability of A given B, P(A|B), or B given A, P(B|A):

$P\left(A\wedge B\right)=P\left(A|B\right)P\left(B\right)=P\left(B|A\right)P\left(A\right).$

(3.1)

The Bayes theorem is derived from Equation 3.1:

$P(A|$