Analysis of large sparse graphs using regular decomposition of graph distance matrices

Hannu Reittu; Lasse Leskelä; Marco Fiorucci; Tomi Räty

doi:10.1109/BigData.2018.8622118

Analysis of large sparse graphs using regular decomposition of graph distance matrices

Hannu Reittu, Lasse Leskelä, Marco Fiorucci, Tomi Räty

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

3 Citations (Scopus)

72 Downloads (Pure)

Abstract

Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into disjoint groups based on observed graph distances from a set of reference nodes. The resulting partition provides a low-dimensional approximation of the full distance matrix which helps to reveal global structural properties of the graph using only small samples of the distance matrix. The presented algorithm is inspired by the information-theoretic minimum description principle. We investigate the performance of this algorithm for selected real data sets and for synthetic graph data sets generated using stochastic block models and power-law random graphs, together with analytical considerations for sparse stochastic block models with bounded average degrees.

Original language	English
Title of host publication	2018 IEEE International Conference on Big Data (Big Data)
Publisher	IEEE Institute of Electrical and Electronic Engineers
Pages	3784-3792
ISBN (Electronic)	978-1-5386-5035-6
ISBN (Print)	978-1-5386-5036-3, 978-1-5386-5034-9
DOIs	https://doi.org/10.1109/BigData.2018.8622118
Publication status	Published - 22 Jan 2019
MoE publication type	A4 Article in a conference publication
Event	Advances in High Dimensional Big Data: Workshop in conjunction with the 2018 IEEE International Conference on Big Data (IEEE Big Data 2018) - Seattle, United States Duration: 10 Dec 2018 → 13 Dec 2018

Workshop

Workshop	Advances in High Dimensional Big Data
Country/Territory	United States
City	Seattle
Period	10/12/18 → 13/12/18

Keywords

graph theory
statistical analysis
Big Data
peer-to-peer computing
partitioning
approximation algorithms
stochastic processes

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10.1109/BigData.2018.8622118

Analysis of large sparse graphs using regular decomposition of graph distance matricesAccepted author manuscript, 3.82 MB

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title = "Analysis of large sparse graphs using regular decomposition of graph distance matrices",

abstract = "Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into disjoint groups based on observed graph distances from a set of reference nodes. The resulting partition provides a low-dimensional approximation of the full distance matrix which helps to reveal global structural properties of the graph using only small samples of the distance matrix. The presented algorithm is inspired by the information-theoretic minimum description principle. We investigate the performance of this algorithm for selected real data sets and for synthetic graph data sets generated using stochastic block models and power-law random graphs, together with analytical considerations for sparse stochastic block models with bounded average degrees.",

keywords = "graph theory, statistical analysis, Big Data, peer-to-peer computing, partitioning, approximation algorithms, stochastic processes",

author = "Hannu Reittu and Lasse Leskel{\"a} and Marco Fiorucci and Tomi R{\"a}ty",

note = "Funding Information: This work was supported by ECSEL-MegaMaRT2 project. Publisher Copyright: {\textcopyright} 2018 IEEE. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.; Advances in High Dimensional Big Data : Workshop in conjunction with the 2018 IEEE International Conference on Big Data (IEEE Big Data 2018) ; Conference date: 10-12-2018 Through 13-12-2018",

year = "2019",

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doi = "10.1109/BigData.2018.8622118",

language = "English",

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Reittu, H, Leskelä, L, Fiorucci, M & Räty, T 2019, Analysis of large sparse graphs using regular decomposition of graph distance matrices. in 2018 IEEE International Conference on Big Data (Big Data)., 8622118, IEEE Institute of Electrical and Electronic Engineers, pp. 3784-3792, Advances in High Dimensional Big Data, Seattle, United States, 10/12/18. https://doi.org/10.1109/BigData.2018.8622118

Analysis of large sparse graphs using regular decomposition of graph distance matrices. / Reittu, Hannu; Leskelä, Lasse; Fiorucci, Marco; Räty, Tomi.

2018 IEEE International Conference on Big Data (Big Data). IEEE Institute of Electrical and Electronic Engineers, 2019. p. 3784-3792 8622118.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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AU - Reittu, Hannu

AU - Leskelä, Lasse

AU - Fiorucci, Marco

AU - Räty, Tomi

PY - 2019/1/22

Y1 - 2019/1/22

N2 - Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into disjoint groups based on observed graph distances from a set of reference nodes. The resulting partition provides a low-dimensional approximation of the full distance matrix which helps to reveal global structural properties of the graph using only small samples of the distance matrix. The presented algorithm is inspired by the information-theoretic minimum description principle. We investigate the performance of this algorithm for selected real data sets and for synthetic graph data sets generated using stochastic block models and power-law random graphs, together with analytical considerations for sparse stochastic block models with bounded average degrees.

AB - Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into disjoint groups based on observed graph distances from a set of reference nodes. The resulting partition provides a low-dimensional approximation of the full distance matrix which helps to reveal global structural properties of the graph using only small samples of the distance matrix. The presented algorithm is inspired by the information-theoretic minimum description principle. We investigate the performance of this algorithm for selected real data sets and for synthetic graph data sets generated using stochastic block models and power-law random graphs, together with analytical considerations for sparse stochastic block models with bounded average degrees.

KW - graph theory

KW - statistical analysis

KW - Big Data

KW - peer-to-peer computing

KW - partitioning

KW - approximation algorithms

KW - stochastic processes

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M3 - Conference article in proceedings

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BT - 2018 IEEE International Conference on Big Data (Big Data)

PB - IEEE Institute of Electrical and Electronic Engineers

T2 - Advances in High Dimensional Big Data

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ER -

Analysis of large sparse graphs using regular decomposition of graph distance matrices

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