  The concepts of similarity and distance are crucial in data mining. We
consider the problem of defining the distance between two data sets by
comparing summary statistics computed from the data sets. The initial
definition of our distance is based on geometrical notions of certain sets of
distributions. We show that this distance can be computed in cubic time and
that it has several intuitive properties. We also show that this distance is
the unique Mahalanobis distance satisfying certain assumptions. We also
demonstrate that if we are dealing with binary data sets, then the distance can
be represented naturally by certain parity functions, and that it can be
evaluated in linear time. Our empirical tests with real world data show that
the distance works well.
