  There is a wide variety of data mining methods available, and it is generally
useful in exploratory data analysis to use many different methods for the same
dataset. This, however, leads to the problem of whether the results found by
one method are a reflection of the phenomenon shown by the results of another
method, or whether the results depict in some sense unrelated properties of the
data. For example, using clustering can give indication of a clear cluster
structure, and computing correlations between variables can show that there are
many significant correlations in the data. However, it can be the case that the
correlations are actually determined by the cluster structure.
  In this paper, we consider the problem of randomizing data so that previously
discovered patterns or models are taken into account. The randomization methods
can be used in iterative data mining. At each step in the data mining process,
the randomization produces random samples from the set of data matrices
satisfying the already discovered patterns or models. That is, given a data set
and some statistics (e.g., cluster centers or co-occurrence counts) of the
data, the randomization methods sample data sets having similar values of the
given statistics as the original data set. We use Metropolis sampling based on
local swaps to achieve this. We describe experiments on real data that
demonstrate the usefulness of our approach. Our results indicate that in many
cases, the results of, e.g., clustering actually imply the results of, say,
frequent pattern discovery.
