### Abstract

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.

Original language | English |
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Article number | 13786 |

Journal | Scientific Reports |

Volume | 5 |

DOIs | |

Publication status | Published - Sep 8 2015 |

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### ASJC Scopus subject areas

- General

### Cite this

*Scientific Reports*,

*5*, [13786]. https://doi.org/10.1038/srep13786

**A unified data representation theory for network visualization, ordering and coarse-graining.** / Kovács, István A.; Mizsei, Réka; Csermely, P.

Research output: Contribution to journal › Article

*Scientific Reports*, vol. 5, 13786. https://doi.org/10.1038/srep13786

}

TY - JOUR

T1 - A unified data representation theory for network visualization, ordering and coarse-graining

AU - Kovács, István A.

AU - Mizsei, Réka

AU - Csermely, P.

PY - 2015/9/8

Y1 - 2015/9/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84941121481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941121481&partnerID=8YFLogxK

U2 - 10.1038/srep13786

DO - 10.1038/srep13786

M3 - Article

VL - 5

JO - Scientific Reports

JF - Scientific Reports

SN - 2045-2322

M1 - 13786

ER -