# Simple question about multivariate/multiclass classification

From this link Text Classiﬁcation using Naive Bayes, there are two models described for classification, Naive and Bernoulli. My question is if i want to make this classifiers for multiclass (multivariate) classification i should use techniques like: one vs. one/rest and etc?

Instead of one-by-one comparison, why not characterizing the entire probability distribution. Let $p(c_i | n, \vec{\theta}_i)$ be the posterior probability that the new observation $n$ belongs to a class $c_i$, then according to the Bayes' theorem:
where $M$ is number of classes which can be in general bigger than two. Having the above probability distribution, you can decide on class assignment for an item $n$ according to the maximum posterior probability. Note that the likelihood function $p(n | c_i, \vec{\theta}_i)$ can be set according to what modeling technique you're going to use. For example, for a Naive Bayes classifier, the features $\vec{\theta}_i$ are assumed to be independent.