  Parallel coordinate plots (PCPs) are among the most useful techniques for the
visualization and exploration of high-dimensional data spaces. They are
especially useful for the representation of correlations among the dimensions,
which identify relationships and interdependencies between variables. However,
within these high-dimensional spaces, PCPs face difficulties in displaying the
correlation between combinations of dimensions and generally require additional
display space as the number of dimensions increases. In this paper, we present
a new technique for high-dimensional data visualization in which a set of
low-dimensional PCPs are interactively constructed by sampling user-selected
subsets of the high-dimensional data space. In our technique, we first
construct a graph visualization of sets of well-correlated dimensions. Users
observe this graph and are able to interactively select the dimensions by
sampling from its cliques, thereby dynamically specifying the most relevant
lower dimensional data to be used for the construction of focused PCPs. Our
interactive sampling overcomes the shortcomings of the PCPs by enabling the
visualization of the most meaningful dimensions (i.e., the most relevant
information) from high-dimensional spaces. We demonstrate the effectiveness of
our technique through two case studies, where we show that the proposed
interactive low-dimensional space constructions were pivotal for visualizing
the high-dimensional data and discovering new patterns.
