# Chinese Restaurant Process… Why?

I recently started to study non-parametric clustering methods and I come across to CRP. After reading all the material I found on the web there is one thing which is not completely clear to me: which is the aim of this process? You can't cluster according to 'distance' (and in fact it was invented another method called Distance Dependent CRP), so why should someone apply this technique? Being a 'noob' I am sure I am missing something... What?

So, you don't have to specify how many clusters there are, which is why it's 'non-parametric'. You do have to specify the probability of each new sample being assigned to a new cluster however, so there is a parameter for that, eg alpha.
Then, you use the DP ("Dirichlet Process") as part of a model, feed it data, and use some way to solve the model. Typically, the model is analytically non-tractable, so one can use Markov Chain Monte Carlo or Variational Approximation to solve it, and get some estimation of the number of clusters, given the data, and the alpha parameter.