  The latent block model is used to simultaneously rank the rows and columns of
a matrix to reveal a block structure. The algorithms used for estimation are
often time consuming. However, recent work shows that the log-likelihood ratios
are equivalent under the complete and observed (with unknown labels) models and
the groups posterior distribution to converge as the size of the data increases
to a Dirac mass located at the actual groups configuration. Based on these
observations, the algorithm $Largest$ $Gaps$ is proposed in this paper to
perform clustering using only the marginals of the matrix, when the number of
blocks is very small with respect to the size of the whole matrix in the case
of binary data. In addition, a model selection method is incorporated with a
proof of its consistency. Thus, this paper shows that studying simplistic
configurations (few blocks compared to the size of the matrix or very
contrasting blocks) with complex algorithms is useless since the marginals
already give very good parameter and classification estimates.
