  Efficient explorative data analysis systems must take into account both what
a user knows and wants to know. This paper proposes a principled framework for
interactive visual exploration of relations in data, through views most
informative given the user's current knowledge and objectives. The user can
input pre-existing knowledge of relations in the data and also formulate
specific exploration interests, which are then taken into account in the
exploration. The idea is to steer the exploration process towards the interests
of the user, instead of showing uninteresting or already known relations. The
user's knowledge is modelled by a distribution over data sets parametrised by
subsets of rows and columns of data, called tile constraints. We provide a
computationally efficient implementation of this concept based on constrained
randomisation. Furthermore, we describe a novel dimensionality reduction method
for finding the views most informative to the user, which at the limit of no
background knowledge and with generic objectives reduces to PCA. We show that
the method is suitable for interactive use and is robust to noise, outperforms
standard projection pursuit visualisation methods, and gives understandable and
useful results in analysis of real-world data. We provide an open-source
implementation of the framework.
