Definitions that I am considering: A generative model learns p(x,y) whereas a discriminative model learns p(y|x=x).
I would like to verify if my understanding is correct by sharing the following claims. Please let me know if my claims are right or wrong (do provide counter-examples).
Claim 1: All generative models are learnt using unsupervised learning.
Claim 2: Not every unsupervised learning algorithm is a generative model. For example, clustering algorithm is not a generative model.
Claim 3: All discriminative models are learnt using supervised learning.
Claim 4: Every supervised learning algorithm is a discriminative model.