I'm reading <http://machinelearning.wustl.edu/mlpapers/paper_files/BleiNJ03.pdf> and trying to understand the notation and concepts behind LDA, in order to implement it myself. I've followed some tutorials about the Poisson and Dirichlet distribution but I'm not super comfortable with them as topics yet.

Can someone explain what is meant on page 4 of the PDF:

> 
> LDA assumes the following generative process for each document w in a
>  corpus D:
> 
> 
> 1. Choose N ~ Poisson(ξ).
> 2. Choose θ ~ Dir(α).
> 
> 
> 

What are these symbols referring to? Extracting words from the Poisson Distribution? How is that even possible? And extracting parameters from a Dirichlet distribution is equally confusing.