A unified data representation theory for network visualization, ordering and coarse-graining.
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.
Wigner Research Centre, Institute for Solid State Physics and Optics, H-1525 Budapest, P.O.Box 49, Hungary.|Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary.|Center for Complex Networks Research and Department of Physics, Northeastern University, 177 Huntington Avenue, Boston, MA 02115, USA.
István A
IA
Kovács
Institute of Organic Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Pusztaszeri út 59-67, H-1025 Budapest, Hungary.
Réka
R
Mizsei
Department of Medical Chemistry, Semmelweis University, H-1444 Budapest, P.O.Box 266, Hungary.
Péter
P
Csermely