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Are Bayesian approaches (static and dynamic) used for classification (which is supervised) or for clustering (which is unsupervised)? or can they be used for both ?

I even see that for instance to compute the likelihood they need the class labels of data, so I was thinking that it is only convenient for supervised cases where we have the class labels

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Well, you can obviously use Bayesian approaches for various things, so why would they not be usable for learning? Also I recommend looking at clustering NOT from a learning perspective. It is not about learning (as in "recall") but about exploration. Many clustering methods will not "learn" anything, they are nothing but a (useful) statistical method. Don't follow the AI view, which is very biased towards machine learning. – Anony-Mousse Sep 25 '12 at 10:44
@Anony-Mousse I didn't talked about "learning", my question was edited by someone else. I want to know if this approaches are more convenient for supervised classification, or rather they more convenient for the unsupervised one (clustering). – shn Sep 25 '12 at 11:42
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What I'm say is that "the unsupervised one" is actually something quite different. It is not classification, because there are no classes, you want to find something new instead. Just my 2¢. Nevertheless, you can use Bayesian approaches for just about anything, your question is too imprecise. – Anony-Mousse Sep 25 '12 at 13:36
@Anony-Mousse which "something new" will you find with clustering ? for me it is like an unsupervised classification. Do you have some concrete examples on "somethings new" that you can find ? Nevertheless, concerning the Bayesian approaches, I even see that for instance to compute the likelihood they need the class labels of data, so I was thinking that it is only convenient for supervised cases where we have the class labels. – shn Sep 25 '12 at 20:11
It's in how you use the data. This is entirely different. In classification, you want to assign objects to the existing classes. In clustering, you want to analyze the clusters found, whether they make any sense to you. So the value is not in single objects being assigned one way or another, but in the global structure. And you want to find structure that you did not know before, to get insight on your data. The most similar thing probably is decision trees, here you also get insight on your data by actually looking at the tree. – Anony-Mousse Sep 25 '12 at 22:50
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Bayesian methods are very general. While there obviously is Naive Bayes, it can of course be used outside the "labeled data" domains.

Bayesian statistic is often defined on sets. The sets could be labels, but they could also be anything else. I figure you could use Bayesian statistics to test for mutual information, for example. So this common use of statistics - sets or predicates, and probably generalizable to fuzzy sets - can be used in various disciplines. After all, I can define predicates such as $x_3 < 7$ and then talk about the probability $P(x_5 > 3 | x_3 < 7)$ depending on a prior of $P(x_3 < 7)$ etc.

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