  Interactions are patterns between several attributes in data that cannot be
inferred from any subset of these attributes. While mutual information is a
well-established approach to evaluating the interactions between two
attributes, we surveyed its generalizations as to quantify interactions between
several attributes. We have chosen McGill's interaction information, which has
been independently rediscovered a number of times under various names in
various disciplines, because of its many intuitively appealing properties. We
apply interaction information to visually present the most important
interactions of the data. Visualization of interactions has provided insight
into the structure of data on a number of domains, identifying redundant
attributes and opportunities for constructing new features, discovering
unexpected regularities in data, and have helped during construction of
predictive models; we illustrate the methods on numerous examples. A machine
learning method that disregards interactions may get caught in two traps:
myopia is caused by learning algorithms assuming independence in spite of
interactions, whereas fragmentation arises from assuming an interaction in
spite of independence.
