I decided to write a different question as a follow up to a comment here about LDA :
I am trying to read about latent dirichlet allocation here : https://web.archive.org/web/20120207011313/http://jmlr.csail.mit.edu/papers/volume3/blei03a/blei03a.pdf .
and I wanted to understand the comment on page 997 :
It is important to distinguish LDA from a simple Dirichlet-multinomial clustering model. A classical clustering model would involve a two-level model in which a Dirichlet is sampled once for a corpus, a multinomial clustering variable is selected once for each document in the corpus, and a set of words are selected for the document conditional on the cluster variable. As with many clustering models, such a model restricts a document to being associated with a single topic. LDA, on the other hand, involves three levels, and notably the topic node is sampled repeatedly within the document. Under this model, documents can be associated with multiple topics.
So the graphical model of LDA is:
, where $M$ is the number of documents and $N$ the number of words in a document (should be equal to the image in the article).
QUESTION: Is the Dirichlet-multinomial clustering model that the paragraph refers to the modification :
so that the only difference is that all words in a document are sampled from the same topic ???? My main issue is that I do not know this clustering model and to me is not simple, quoting the text, hence my doubt that I am not getting the point ... at least to me is not simpler than vanilla LDA...