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

TL;DR

This paper introduces an information theoretic framework that unifies network visualization, data ordering, and coarse-graining, enabling efficient analysis and hierarchical visualization of large complex data sets.

Contribution

The paper presents a novel unified theoretical approach based on relative entropy for representing data, linking visualization, ordering, and coarse-graining tasks.

Findings

Provides an optimal data representation method based on indistinguishability from original data.

Enables efficient visualization and ordering of network nodes as probability distributions.

Facilitates hierarchical data compression and visualization for large data sets.

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.