Multinomial Naive Bayes
Multinomial Naive Bayes is one of the two classic Naive Bayes variants used in text classification.
P(x_i | y)
of features i
appearing in sample belonging to class y
is:
(Ny_i + alpha)/(Ny + alpha * n)
where:
Ny_i
=Sum(x_i)
the number of times featurei
appears in a sample of classy
in the training set.Ny = Sum(Ny_i)
is the total count of all features for classy
.
The training algorithm is typically very fast, and it is able to produce relatively good prediction performance when:
- The training set is relatively small (dozens of samples per class).
- Training and test data are internally well balanced (the different classes are equally represented in the data distribution).
- Dataset are mainly made of equally sized documents.