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Representation of large data sets became a key question of many scientificdisciplines in the last decade. Several approaches for network visualization,data ordering and coarse-graining accomplished this goal. However, there was nounderlying theoretical framework linking these problems. Here we show anelegant, information theoretic data representation approach as a unifiedsolution of network visualization, data ordering and coarse-graining. Theoptimal representation is the hardest to distinguish from the original datamatrix, measured by the relative entropy. The representation of network nodesas probability distributions provides an efficient visualization method and, inone dimension, an ordering of network nodes and edges. Coarse-grainedrepresentations of the input network enable both efficient data compression andhierarchical visualization to achieve high quality representations of largerdata sets. Our unified data representation theory will help the analysis ofextensive data sets, by revealing the large-scale structure of complex networksin a comprehensible form.

A unified data representation theory for network visualization, ordering and coarse-graining