  A good clustering can help a data analyst to explore and understand a data
set, but what constitutes a good clustering may depend on domain-specific and
application-specific criteria. These criteria can be difficult to formalize,
even when it is easy for an analyst to know a good clustering when they see
one. We present a new approach to interactive clustering for data exploration
called TINDER, based on a particularly simple feedback mechanism, in which an
analyst can reject a given clustering and request a new one, which is chosen to
be different from the previous clustering while fitting the data well. We
formalize this interaction in a Bayesian framework as a method for prior
elicitation, in which each different clustering is produced by a prior
distribution that is modified to discourage previously rejected clusterings. We
show that TINDER successfully produces a diverse set of clusterings, each of
equivalent quality, that are much more diverse than would be obtained by
randomized restarts.
