Fast computation of von Neumann entropy for large-scale graphs via quadratic approximations
Information Theory
2019-07-23 v2 Data Structures and Algorithms
Social and Information Networks
Signal Processing
math.IT
Data Analysis, Statistics and Probability
Abstract
The von Neumann graph entropy (VNGE) can be used as a measure of graph complexity, which can be the measure of information divergence and distance between graphs. However, computing VNGE is extensively demanding for a large-scale graph. We propose novel quadratic approximations for fast computing VNGE. Various inequalities for error between the quadratic approximations and the exact VNGE are found. Our methods reduce the cubic complexity of VNGE to linear complexity. Computational simulations on random graph models and various real network datasets demonstrate superior performance.
Keywords
Cite
@article{arxiv.1811.11087,
title = {Fast computation of von Neumann entropy for large-scale graphs via quadratic approximations},
author = {Hayoung Choi and Jinglian He and Hang Hu and Yuanming Shi},
journal= {arXiv preprint arXiv:1811.11087},
year = {2019}
}