  Representation of large data sets became a key question of many scientific
disciplines in the last decade. Several approaches for network visualization,
data ordering and coarse-graining accomplished this goal. However, there was no
underlying theoretical framework linking these problems. Here we show an
elegant, information theoretic data representation approach as a unified
solution of network visualization, data ordering and coarse-graining. The
optimal representation is the hardest to distinguish from the original data
matrix, measured by the relative entropy. The representation of network nodes
as probability distributions provides an efficient visualization method and, in
one dimension, an ordering of network nodes and edges. Coarse-grained
representations of the input network enable both efficient data compression and
hierarchical visualization to achieve high quality representations of larger
data sets. Our unified data representation theory will help the analysis of
extensive data sets, by revealing the large-scale structure of complex networks
in a comprehensible form.
