  In the framework of model-based clustering, a model, called multi-partitions
clustering, allowing several latent class variables has been proposed. This
model assumes that the distribution of the observed data can be factorized into
several independent blocks of variables, each block following its own mixture
model. In this paper, we assume that each block follows a non parametric latent
class model, {\it i.e.} independence of the variables in each component of the
mixture with no parametric assumption on their class conditional distribution.
The purpose is to deduce, from the observation of a sample, the number of
blocks, the partition of the variables into the blocks and the number of
components in each block, which characterise the proposed model. By following
recent literature on model and variable selection in non-parametric mixture
models, we propose to discretize the data into bins. This permits to apply the
classical multi-partition clustering procedure for parametric multinomials,
which are based on a penalized likelihood method (\emph{e.g.} BIC). The
consistency of the procedure is obtained and an efficient optimization is
proposed. The performances of the model are investigated on simulated data.
