  Deciding whether the results of two different mining algorithms provide
significantly different information is an important, yet understudied, open
problem in exploratory data mining. Whether the goal is to select the most
informative result for analysis, or to decide which mining approach will most
likely provide the most novel insight, it is essential that we can tell how
different the information is that different results by possibly different
methods provide.
  In this paper we take a first step towards comparing exploratory data mining
results on binary data. We propose to meaningfully convert results into sets of
noisy tiles, and compare between these sets by Maximum Entropy modelling and
Kullback-Leibler divergence, well-founded notions from Information Theory. We
so construct a measure that is highly flexible, and allows us to naturally
include background knowledge, such that differences in results can be measured
from the perspective of what a user already knows. Furthermore, adding to its
interpretability, it coincides with Jaccard dissimilarity when we only consider
exact tiles.
  Our approach provides a means to study and tell differences between results
of different exploratory data mining methods. As an application, we show that
our measure can also be used to identify which parts of results best redescribe
other results. Furthermore, we study its use for iterative data mining, where
one iteratively wants to find that result that will provide maximal novel
information. Experimental evaluation shows our measure gives meaningful
results, correctly identifies methods that are similar in nature, automatically
provides sound redescriptions of results, and is highly applicable for
iterative data mining.
