Bayesian classifiers
The naive Bayes classification algorithm is a classification process that is based upon Bayes' Theorem, which we examined in Chapter 4, Statistics. It is embodied in the formula:
where E and F are events with probabilities P(E) and P(F), is the conditional probability of E given that F is true, and P(F|E) is the conditional probability of F given that E is true. The purpose of this formula is to compute one conditional probability, P(E|F), in terms of its reverse conditional probability P(F|E).
In the context of classification analysis, we assume the population of data points is partitioned into m disjoint categories, C1, C2,..., Cm. Then, for any data point x and any specified category Ci:
The Bayesian algorithm predicts which category Ci the point x is most likely to be in; that is, finding which Ci maximizes P(Ci| x ). But we can see from the formula that that will be the same Ci that maximizes P( x |Ci)P(Ci), since the denominator P(x) is constant.
So that's the algorithm...
