I have implemented a naive bayes classifier for a multivariate Gaussian distribution. I have 3 classes, C1, C2 and C3.

I know P(error) is defined as the number of items that were classified incorrectly divided by the total number of items – for instance the number of times a items that belonged to class 1 were assigned labels for class 2 or 3.

A simple way to compute the P(error) numerically would be to compute the confusion matrix first and then just sum the number of elements assigned incorrectly.

The total probability error would be: P(error)_C1 P(error)_C2 P(error)_C2

I have confusion about what number to divide by – should I divide by the total number of items in the data-set or divide each sum by the total number of items for that particular class i.e.:

Should it be:

P(error)_C1 = number of items classified as C2 and C3 / total items in the dataset

or

P(error)_C1 = number of items classified as C2 and C3 / total items in C1