  We address the problem of data clustering by introducing an unsupervised,
parameter free approach based on maximum likelihood principle. Starting from
the observation that data sets belonging to the same cluster share a common
information, we construct an expression for the likelihood of any possible
cluster structure. The likelihood in turn depends only on the Pearson's
coefficient of the data. We discuss clustering algorithms that provide a fast
and reliable approximation to maximum likelihood configurations. Compared to
standard clustering methods, our approach has the advantages that i) it is
parameter free, ii) the number of clusters need not be fixed in advance and
iii) the interpretation of the results is transparent. In order to test our
approach and compare it with standard clustering algorithms, we analyze two
very different data sets: Time series of financial market returns and gene
expression data. We find that different maximization algorithms produce similar
cluster structures whereas the outcome of standard algorithms has a much wider
variability.
