The Chinese Restaurant Process (CRP) is one possible representation of the Dirichlet Process.
The metaphor works as follows:

- We have a Chinese restaurant with infinitely many tables. At the start of the day, the restaurant is empty.
- When the first guest enters the restaurant, he sits at a new table and orders a dish.
- Each new guest who enters afterwards will start either a new table with probability \(\frac{a}{a+n_k} \) or decide to sit at the already occupied table \( k \) with probability \( \frac{n}{a+n_k} \)

How does the number of tables grow with the number of customers? The answer is logarithmically. We have that
\( \mathbb{E}(K) = O \left(\alpha \log(n) \right) \)