Is naive Bayes supervised or unsupervised?

First, Naive Bayes is not one algorithm but a family of Algorithms that inherits the following attributes:

1.Discriminant Functions

2.Probabilistic Generative Models

3.Bayesian Theorem

4.Naive Assumptions of Independence and Equal Importance of feature vectors.

Moreover, it is a special type of Supervised Learning algorithm that could do simultaneous multi-class predictions (as depicted by standing topics in many news apps).

Since these are generative models, so based upon the assumptions of the random variable mapping of each feature vector these may even be classified as Gaussian Naive Bayes, Multinomial Naive Bayes, Bernoulli Naive Bayes, etc.